My level one tenants all seem to start fires at the same time, with very little or no provocation.
This is something I despise about the game. Instead of being sophisticated, it simply exploits the frailties of human reaction time. You cannot be everywhere at once, and it deliberately throws too many things at you at one time.
That's not clever. That's not fun. That's not good game design. That's brute-force crap on a level with an arcade game like Pac Man.
That said, the theme is so much fun, I will probably keep playing......but, can anyone suggest how to put out fires? I've got repairmen assigned to the blocks where they happen, and evidently that isn't enuough. Can you put out a fire by satisfying the demands that precipitated the fires?

It's been a while since I played Constructor (currently waiting for my PayPal account to update so I can buy the game here), but I think I can help you out.
Fires only start if your houses aren't maintained regularly. Repairmen have an "automatic" setting where they patrol one or several blocks of houses and repair the buildings. This can be done manually, but is very time consuming.
If all your houses catch fire at the same time, my guess is that you selected the repairman and sent them to some houses, but didn't actually tell them to do something. Try checking for the auto-repair / patrol feature.

Actually - if the repairman gets INTO the house (gray flag outside) - he will know what to do. Autorepairs are very useful, though keep in mind that the repairman will go around visiting buildings ONLY on the estate he got the auto-repair order. To change the estate he's patroling, simply send him to a house on another one.
Also - houses get a lot more torn up if the tenants inside are pissed off... I'm sure you can imagine why ;P. To prevent this - either keep them happy or upgrade their lounge.
Still - even with the happiest tenants on Earth - houses will still degrade. You can slow this process down A LOT by upgrading the bathroom.

If you find constructor's too hard for you, do a barrel roll.

You can also provide your tenants with toolboxes from the gadget factory so that they can repair the house themselves (haven't tried it yet, but that's what it says it does).
Also, I've noticed that repair men don't repair undesireables. Not sure if this is deliberate, but the only thing I can do with them is use the manual repair feature and spend the money.

...or blow them up and rebuild. At some point it actually becomes less expensive.

I've also noticed that repairman does not repair "Commune" building. If I send him in this building, he almost immediately leaves it. Only manual repair helps.
Does anybody have this problem, or I am doing something wrong?

Communes are one of the "undesirable" buildings that wpegg was talking about - this doesn't just affect communes, but apartments, mob buildings, etc.
As Vestin suggested, it may be cheaper to actually blow these buildings up instead of using the "manual repair" button - especially if you aren't planning to use that undesirable in the near future.

Yes, this seems to be a bug in the game.
The repairman never autorepairs undersirables' abodes. If you own 8 UND's it's a pain in the ass to keep manually repairing them everytime. I think this must be a bug in the game.