By RAW, it depends on what you are crafting; Yes, for some things.
As per the "Tool Proficiencies" section in Xanathar's Guide to Everything (starting on p. 78), with the correct tools many things can be crafted during rest periods. Each of these are specifically mentioned in RAW.
You can make basic alchemical materials like acid, alchemist's fire, antitoxin, or soap during a long rest.
Ditto a meal or a forged document takes a short rest.
Repairing metalwork, so smithing, can be done at 10 HP per hour but stipulates you need to have a hot enough flame to soften the metal, which in the real world means you need a forge wagon to do while afield, but here might be accomplished with magic.
Clothing can be created during a long rest, or repaired during a short one.
Arrows can be crafted during a short or long rest with woodcarver's tools.
Crafting a map is directly stated to something that can be done while traveling with cartographer's tools.
Painting and drawing is stated to be doable during rest periods.
Crafting also falls under the downtime activity rules (Xanathar's, p. 128), 50 gp value per 40 hrs of work, including some of the above as examples, implying some overlap and allowing us to compare time and progress.
The implication is clear anything you might reasonably be able to do with the tools on hand, you can do it, but other things are nigh impossible because the equipment or material is not portable. Notably masonry, glassblowing, and leatherworking lack any mention of rest activities which makes sense since these each require significant time and non-portable equipment or are themselves not portable (note in the real world harvesting a hide is very different from turning it into leather). Even smithing only allows for repairs with a big qualifier attached.
To use arrows as an example (XGE, "Woodcarver's Tools", p. 85), you can create 20 arrows during a long rest or 5 during a short rest, using downtime crafting 20 arrows takes about an hour (1 gp, 0.8 hours), so there is definitely an implication that crafting on the go takes a lot longer, about 4 times as long when it is possible at all. This makes sense since you would not be able to devote your full time and effort into it.
Yet something like an 50 gp antitoxin also takes a long rest (XGE, "Alchemical Crafting", p. 79), presumably because the cost reflects material cost not labor, which makes sense given the cost of raw materials given (50 gp per pound).
So it is up to the GM whether it is possible (do you have the necessary tools and raw material). How much you get done is not well-defined, but a good rule of thumb might be 1 gp worth of labor per long rest. Keep in mind that D&D is not supposed to be a high-fidelity life simulator; just because it doesn't talk about it does not mean you can't do it. Nowhere does it tell you you can bathe or how to construct a campfire either, yet few would argue you can't do these activities.
Specific Rules Apply - RAW
By Rules as Written, a mount is a mount. A mount follows the rules for mounts in the Player Handbook/Basic Rules/SRD. Infernal Machines are from Descent and don't use mount rules, even if the rules are similar, they are different things.
Mounted Combatant Feat - Houserule
While this, RAW, doesn't apply to infernal machines, as above, I don't think that it would be game breaking for a feat with almost identical rules to exist/house rule for infernal machines. I've seen a game with pistols that applied this idea to Crossbow Expert. I think if the new thing is similar enough there isn't harm in trying it -- with strict explanation to the players that since it is off book, you reserve the right to alter or amend the houserule.
I'd be temped to make it its own feat as expertise in riding a horse in real life doesn't make you a good driver, and being a NASCAR driver doesn't make you good at riding a horse. Moreover, if the house rule is found to be problematic for infernal machines you can tweek just the language of the new feat without messing with mounts. Remember, Jeremy Crawford explains the 5e philosophy as "rules of exceptions" based on the idea that new stuff shouldn't break or change old stuff.
Best Answer
Distances are determined by the DM--and don't have to be consistent
In the Introduction, it says this
The section on using the map says...
and
In short, the only one who can determine how far it is from Point A to B in Avernus is the DM. Things are not always in the same place you left them. Even if you are trying to return to the same location you've been to before, there's a chance you'll end up in entirely the wrong place
Maybe today it takes two hours to get from the Bone Brambles to the Arches of Ulloch, and you get there by traveling "North West." But the next time you make the trip, it takes three days and you have to travel in an entirely different direction to get there.
So, to put it simply...
The map is a crude guideline made by an increasingly crazy person. It is not reliable, and it gives no indication of the distance between points. Whenever players choose to travel within Avernus, it is up to the DM to decide how far they have to go and how long they have to travel.
Descent into Avernus offers no guidelines beyond this.
Aside
Where you say...
Note that this is an optional rule provided for DMs to add to the game if they want to.
TL;DR:
It is entirely up to the DM to determine distances between two locations, because "location" is more of a suggestion in Avernus than an actual rule. And the distances do not always have to be the same twice in a row...in fact, it is recommended that they not always be the same.