No.
Consider the following excerpt from the AL FAQ:
What Rules Do I Use
As a D&D Adventurers League Dungeon Master, you are empowered to adjudicate the rules as presented by the official materials (PHB, DMG, MM, etc.). Run the game according to those rules, but you are the final arbiter of any ambiguities that might arise in doing so. (Emphasis mine.)
We see this also in the AL DMG which says in "Playing the Dungeon Master"
You're Empowered. Make decisions about how the group interacts with the adventure; adjusting or improvising is encouraged, so long as you maintain the adventure’s spirit. This doesn’t allow you to implement house rules or change those of the Adventurers League, however; they should be consistent in this regard. (Emphasis mine.)
DMs are simply not allowed to change rules, houserule, or intentionally mis-read rules.
But DaleM first made an excellent point:
The DM is allowed to be wrong!
Most of your examples look like places where your DM has made a mistake. I'd submit, though, that at least in bullets 2 & 4 those are reasonable mistakes to make. In (2) during combat they may not have the complete text of command at the tip of their brain. Likewise for (4) the rules on how adventures continue over sessions aren't referenced very often. We simply don't look over those rules very frequently, so they're not at the tip of the brain. Did they handle it well? Maybe not. Is that understandable? Maybe.
Not only are they allowed to be wrong, I'd expect my AL DM to make mistakes some times. The GM has a lot of chances to make a mistake during a session. We're not going to get every one of them right. I, personally, often lean on my players (half of whom are excellent GMs, too) to keep me on the "straight-and-narrow."
So it comes down to this: what happens when my AL DM is wrong?
You've said "when I told him about the existing rules, he either discarded what I had to say or decided to rule otherwise anyway." I think we're missing an important bit of context here: was that during the middle of an encounter? At the end of a session? Before the beginning of a session? Offline?
There aren't many players whose definition of "fun" is gathering at their FLGS to spectate as two people debate rules while their characters' lives are on pause. I'd suggest that in real time isn't the time to press a disagreement. Raise it once? Sure. But if they don't immediately see your point then jot yourself a note and move on.
Raising rules-questions out-of-session.
Ask your DM if you can chat with them while you help clean up minis and fold up maps. Explain exactly what you said above: you love some things about their style (and are trying to learn from them) but other things make it hard for you. Your understanding of AL is that they're supposed to hew to the rules. You understand they'll make mistakes just like any human, that they have many more opportunities to make mistakes, and their mistakes are more visible/impactful than any others. And ask how you can help.
If that gets nothing, if they show no interest in reducing their error rate, that's when you ask the site coordinator for help.
I agree with GreySage's answer, but as I'm currently playing through LMoP myself, with a group of entirely new players, I wanted to add a bit of extra insight based on my own experiences of this module specifically.
If this doesn't help you, then hopefully it might help others with similar questions, especially if they're DMing for new players. Potential spoilers follow:
Adding more money to treasure hauls will not unbalance this game.
This is primarily for the reason that GreySage stated, particularly in this module 'money is basically useless'. While this treasure hoard may seem small, when they arrive in Phandalin, they have the potential to also get:
- 50 gold from the Lionshield Coster (for reporting the location of their lost supplies)
- 50 gold from Sildar Hallwinter (for escorting him to Phandalin)
- 10 gold each from Barthen's Provisions (for escorting Gundren's supplies)
And, the adventure's generosity doesn't stop there. Your PCs will soon be rolling in more money than they have any use for.
The module does attempt to 'solve' this issue by presenting the players with a potential 'money sink', later, but as most games end soon after, the money is still largely useless. That's unless you decide to keep playing, with these characters, in this world, after the published adventure is complete, in which case, this question about the cost of renovating Tresendar Manor, may be useful to you.
Be wary of removing the health potions
If you're playing using the LMoP pre-generated characters then you'll only have one healer in the party. If they go down, the PCs having a few healing potions handy is invaluable.
Health potions will also help to keep the game moving when it might otherwise grind to a halt. Tresendar Manor, likely the place they'll head next, has potentially 7 combat encounters, some of which could be fairly challenging. So, if you want to maintain some realism, and avoid you party 'short-resting' (or trying to) at every available opportunity, in the middle of enemy strongholds, then keeping a few healing potions could be the solution.
If you want to add an extra item, consider making it a teachable moment
This may not be relevant to your situation, but I'm including it here, just in case it helps you, or anyone else with a similar question later. If you want to roll for magic items then I agree with everything GreySage said.
My players were all completely new to DnD so I wanted to use this first dungeon to teach them a lot of the rules, as we went. For example, the Goblin Ambush was the first time I taught them about turn order and action economy. In this treasure hoard I wanted to teach them about the potential value to be gained from beating the 'boss' and also, mechanically, how the item attunement system worked.
I therefore chose to insert a completely homebrewed item into this hoard (without changing it otherwise). It was something like this:
Fang of the Packleader Wondrous item, uncommon (requires attunement)
This vicious-looking canine tooth must have come from an impressively large wolf. It has had a hole drilled through it and been threaded onto an old ratty piece of string, creating a crude pendant.
Once attuned, this item grants the bearer +1 on all Animal Handling checks and Advantage on Animal Handing and Intimidation checks that relate specifically to Wolves.
Now, whether this item is balanced or not (it was my first attempt at homebrewing anything), is not important here. I wanted it to be something that would thematically fit as being owned by Klarg (who is rather attached to his pet wolf), so that they could find it actually on him, rather than just lying with the other stuff in his hoard.
Including the 'Fang of the Packleader' allowed me to explain how attunement worked, stoke excitement for future treasure, and provide a reward that was slightly more interesting than simple money and health potions. Limiting its usefulness also meant that it wouldn't be gamebreaking. If you don't want to risk homebrewing something for your own game, consider using one of the 'Common Magic Items' from XGTE.
I also wanted to show my players how items that they found could be good plot-hooks for roleplay, character growth, and narrative. So, after a few long rests, I started seeding the idea that the bearer's own canine teeth were lengthening, and that their eyes were slowly turning gold, as they become more wolf-like themselves.
The PCs increasingly more wolf-like appearance provided some fun opportunities for inter- and extra-party roleplay as the campaign went on. Ultimately, later in the campaign, to reward the pleyer for leaning into the changes in his play, once most of the rest of the party had found significantly more useful items, I had the item 'evolve' to provide its bearer 3 uses per long rest of the Wolf's ability 'Pack Tactics'.
Anyway, have fun playing the Lost Mines of Phandelver. Whether you choose to use any of this, or not.
Best Answer
There's no hard-and-fast set of rules on this. But we've got a few ways of looking at your scheme.
1. Crafting (PHB187)/Crafting Magic Items (DMG 128-129). Each of these pursuits allow you to manage your downtime-game to the level of which X are you creating at what times. While crafting mundane items and crafting magical items proceed at different paces (5gp-worth vs. 25 gp-worth each day), in each case we have the following provision: while crafting a [magical] item "you can maintain a modest lifestyle without having to pay 1 gp per day, or a comfortable lifestyle at half the normal cost."
The reasonable read on that is that the PCs labor "earns" them 1gp per day. It's not explicit in the rules, but you could make the argument to your DM that while your work earns you 1gp you could choose to "squeak by" on a semi-modest or even poor lifestyle, pocketing the difference.
2. Practicing a profession (PHB187). But perhaps you're not interested in the exact items you're crafting, you just want to be a smith. The PHB has rules which allow you to abstract your economic activity one layer and practice that profession. At the low end this earns one enough to cover a modest lifestyle (1gp per day), as in the "crafting" rules. But adding a support organization--a guild or, perhaps, your business partners--in your profession allows one to cover a comfortable lifestyle (2gp per day). As in point 1, perhaps there's room to extract profit from living within one's means?
3. Running a business (DMG129). Frankly, though, it sounds like you're capitalists. Big bosses. You own the means of production. You're running a business. Your business has maintenance costs indexed to its size/complexity that you'll have to figure out with your DM. But here's some guidance:
Maintenance Costs (DMG127). I'd estimate that a good half-dozen skilled workers might productively work at your location (based on keyed locations 12 and 15), with some larger number of unskilled workers assisting\$^1\$. This puts your business in the neighborhood of those with 10 gp/day maintenance costs on the low end, squarely in the conversation with businesses requiring 20 and 25 gp/day, and well below those requiring 50+ gp/day. It's assumed that a functional business left alone covers its maintenance costs, but doesn't particularly clear a profit.
Making a Profit. To make a profit on your business you've got to invest some of your time. I'll spare you the details--they're in the DMG--but downtime days spent on your business produce modifiers to a roll for the business's profitability. Assuming a 25 gp/day maintenance-cost business\$^2\$ (see above), your expected gp/day profit ranges from 5 to 39.75 as you devote between 1 and 30 downtime days\$^3\$.
Putting it all together: "what can the PCs expect to earn?"
Epilogue: so why run a business?
Your business is not going to sit there and generate a return for you unless you invest time into it. But it does play the following roles:
1 - This ignores the mine, focusing on the spellforge. As mentioned in note 2, including a mining operation will actually drive down the profitability of your enterprise. But should you wish to include it, the expected returns look like (at 30-day downtime investment) 36gp/day profit for a 100gp/day maintenance operation (ca. 100 workers), 21gp/day profit for a 400gp/day maintenance operation (ca. 300 workers). Diminishing returns, and all....
2 - Not to get too deep into the weeds, but the profitability of businesses diminishes with their size. That's because losses are proportional to maintenance costs, but profits are constant. So it may be incumbent upon an enterprising wealth-manager to consider diversifying business holdings rather than growing, but this'll depend on how you strategically hope to invest your downtime.
3 - The modifier to the business roll plateaus at 30 days.