Background and Legacies
Outside the dungeons, pits, castles and sewers there is the chance to explore what the characters are more than just damage dealing machines, what they want to be their legacies, who they know, what they want to be; encourage players to expand on their backstories - or examine their backgrounds and see what can come out of the woodwork, not even as a battle but as someone to talk to or stories that they can find out about.
Relationships
High level characters should have not a small amount of fame and NPCs should be clamouring to apprentice/advise/woo/get money/kill them depending on what they've become famous for. Think Wizard duels to determine "the greatest magi of the land", building sage towers to tutor a school of magic, creating new religious movements, creating a guild of adventurers to solve all the petty tasks that no longer are worth the time, etc.
The world
At Epic level politics becomes an important factor; characters who are powerful can solve important problems, defeat enemies or swing wars between countries and Kings/Nobles/Wizards will want the PCs on their side - or rid of them - for wider political motives
Think scheming political figures "Have this castle as my thank you for your service" (said castle is crawling with dangerous bandits) religious orders that are asking for help with crusades and so on.
Making it alive
And those the players know will have moved on as well; NPCs shouldn't stand still, give a little snippet to important figures in the characters lives to make things feel more "alive", Bob and Bobette have had a baby, Duke Von Bob has created a new trade route, Trader Bob has partnered with his former enemy anti-Bob.
A world of shops and taverns?
Another thing to help the players feel a place is more alive is to add things to the city that are more than rumour-generation taverns and item-trading shops. Don't scattergun these in, you can drip feed them schools, colleges, magical research centres, masons guilds, graveyards and religious institutes to the point that (hopefully) they'll ask "is there an X" in town and then you can sit back and stuff in some generic NPCs for X, give it a name and have them talk to a piece of the city that they've effectively generated for you. Now that's lazy GM'ing and I like that :)
PC: "Is there an alchemist in the city?"
Me: (Checks list of random npc names, rolls a dice for personality on a quick chart), writes 'Alchemist, gruff, slightly mad, level 15' "Yes there is, a few inquiries tells you about Old Bob the Alchemists shop of chemical wonders, it's down old goat street."
In general, I would suggest not using the Downtime and Kingdom Building rules, since they are generally written very poorly and have a lot of weird edge cases and odd inconsistencies. That said, it sounds like you are having trouble with the dichotomy of capital earned versus capital spent, and also how capital checks work.
The fact that you are in a Small Town only restricts the number of capital you can spend per day. You can earn as much capital as you want each day, with no real limit. If your capital checks say that you can make 500 Magic in a day, then the fact that you are in a town with less than 500 people doesn't stop you. However, it will take over a month to actually spend all of that capital. The line to be aware of is:
The numbers in Table: Settlement Spending Limits represent the limit of how much Goods, Influence, and Labor you can utilize in settlement each day.
Emphasis mine. The Settlement Spending Limits only apply to the amount of capital you can spend, not earn.
In addition, your capital check values are a little off. I'm going to assume that the bonuses for each building that you've calculated are correct, at least for the moment. For each building, you only make one capital check, probably based on the highest bonus that you have for that building, unless you have a reason to want a different kind of capital. Assuming you're going for the highest total capital amounts, your "take 10" values for each building would be:
- Monument: Influence 16
- Tavern: Influence 37
- Hospital: Influence 61
- Castle: Influence 178
This totals 292, for 29 Influence per day. You don't get to make a separate check for each type of capital each day, you only get to pick one at a time. The line to be aware of is from the Income section:
Attempt a capital check (see the Earnings section) for each building you control in the settlement that generates income and is able to provide you benefits.
Emphasis mine. Since a capital check only lets you generate one kind of capital at a time, your buildings can't make multiple kinds of capital at once.
About weekends: The whole 'weekend' thing only applies to Craft and Profession checks made weekly. Honestly, I'm pretty sure that they just put that section in so that they could divide things by 10 without running afoul of the existing craft rules. In real medieval life, there were no such things as weekends. The idea of taking two days off every seven is relatively new, and is sort of a weird thing to add to a system like this. If your GM wants to restrict work to the modern work week, then that's their prerogative, but there isn't anything in the rules that actually says that you can't work or spend capital on the weekend. If your GM doesn't enforce the weekend, you can spend a total of 5475 capital per year in a Small Town. If they do, you can spend 3900, as you note.
This expenditure can be on anything you have the capital for, but must be done in 15-capital increments. If you want to build a structure that costs more than 15 capital, you spend 15 capital each day until you have spent enough capital to build the whole structure. Note this line from the Construct Buildings action:
How much capital you can spend per day is limited by the size of the settlement you're in (see Spending Limits). Once you've spent the total capital and time needed to finish your building, it's complete and you can use it immediately.
You are correct that earning capital only allows you the opportunity to buy that capital. The Skilled Work rules note:
You must pay the Earned Cost to buy this capital, although if you can't afford to buy all of it or don't need more than a certain amount, you can choose to earn less capital than your check indicates.
There isn't a separate section for capital earned using buildings, but I'm pretty sure that buildings are supposed to use the Skilled Work rules. Like you say, if you produce 3,900 Goods, you need to spend 39,000 gp to actually get those goods. Remember, though, that you can produce gp instead of capital, if you want. There's a different bonus for earning gp, but it works pretty much the same way as a normal capital roll: take your results, divide by 10, and that's what you earn in gp.
Best Answer
Question 1) You can make the checks when he goes back, or he can make the checks himself every day. The business works even if the owner isnt there to activelly direct the workers, as it is assumed you hired people to make your business work, and your earnings are your profit after you paid them and the business paid all it's cost. Though, if the hero isnt there, you should apply the 7 days absence penalties as normal, which could ruin the business after a while (which can be fixed with a manager).
Question 2) The manager's job is to prevent the absence penalties and roll for the random events instead of the hero, but the earning checks will happen wether or not the hero is there. Personally, i prefer to roll them after they get back, we count the days away, i roll a couple of random events, see how many checks they have to make, and they take 10 on all of them.
Question 3) As said above, the checks will happen regardless of his presence. But that is a good question because if the hero can communicate at distance, the absence clock is reset everytime he communicates with them. That way they know what to do and they know their boss is still alive.
Question 4) Everything other than GP you will have to pay the half-price for it. If i recall correctly, labor and goods are 20 gp (half price is 10 gp), while influence is 30 gp (half price is 15 gp), and magic is 100 gp (half price is 50 gp). So, when you are earning capital you dont gain any GP, but you are not actually losing any either, because the price for rooms and hirelings are based on the full cost of the capital, so if you take your time to earn the capital, you can buy things at half the cost. See that as an investment of your money, in the long run you will have discounts to build other rooms and hire more people.