PC's and NPC's pretty much do have the same rules.
Can NPC's have classes? Yes, they can.
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Imagine the annoyance of having different combat rules for PC's and NPC's and then trying to translate for problems like PC's attacking PC's or NPC's attacking NPC's.
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It's in fact simpler and easier to give NPC's the ability to use the same spells available to the PC's
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Of course NPC's have downtime. Arguably, all most NPCs have is downtime!
I think that all this misses [MENTION=22779]Hussar[/MENTION]'s point.
"Downtime" is not an ingame phenomenon. It's a real-world, playing-the-game-at-the-table phenomenon. It's the time in which the PCs are doing stuff but the players at the table are not working through the action and its outcome in any detail.
Hence, it is not a concept that has any application to NPCs, who are - by definition, as it were - not played at the table, except in so far as they are interacting with the PCs.
This also goes to the issue of action resolution for NPCs (combat, spells, etc). If the PCs ride past a field and see two knights jousting, the GM is under no obligation, except in a very strong sim game, to resolve that joust and narrate its outcome by reference to the combat rules. For instance, the GM could narrate one knight being unhorsed by the other and suffering a broken collarbone, although the 5e combat mechanics have no procedure whereby such an outcome could be generated.
As for NPCs having classes, in 5e this is not generally true - for instance, the proficiency bonus for NPCs is a function of CR, not notional class level (eg the 9th level mage on p 55 of the Basic DM Pdf has a +3 proficiency bonus, per CR 6, rather than +4, per level 9). Nor does that mage have all the funky special abilities that a PC wizard of that level would have.
A second stress test of the down time rules is suppose we for whatever reason find ourselves using the downtime rules in place of the campaign. Maybe, for whatever reason, the table agrees to advance the timeline by 10 years and decides to run those 10 years (520 weeks) entirely using the down time rules. If the rules are solid and well thought out, this should produce no difficulty and while the process of playing through 520 steps of down time might not be fun (depending on your taste), if the rules are solid then the net result should be 'believable' in some fashion and describe a career or trajectory that makes some degree of sense for the choices the player made and skills that they have.
To my mind, this is like proposing army vs army combat as a stress test of the 5e combat rules. (Ie it is an implausible proposal.)
If the downtime rules are designed to handle down time of days and weeks - correlating to typical D&D times for healing, spell research etc - it is no blot on their copybook that they do not do a good job of generating the sort of substantive campaign content that you are talking about here.
General size of the stronghold, best with examples (Small keep, large keep, etc.), best with example descriptions. (Sensible) Income/produce examples given for commercial buildings and advice for all building types what they represent is game worlds (FR is default, but when you have space also for alternative settings), what impact they have onto the settings and adventure seeds, best with different levels of spotlight.
Seriously? You are asking for an economics/finance text to be written for the gameworld.
The real world actually happened (and continues to happening), but doing what you ask for in relation to the real world is a full-time occupation for thousands of people just in Australia alone and they often can't get it right. How do you expect it to be done for an an imaginary world which, in economic and social terms, makes no sense once you get below the outermost veneer?