What are the usual "best practices" that we should be following to ensure normal operation during the UPS maintenance window?
Chances are that the mobile generator the building is apparently renting will be quite stable – perhaps more so than units buildings often buy and install for themselves. Companies providing mobile power have to service a variety of customers, so usually use very good, well regulated equipment. There's not guarantee, of course, but since you have alerted your building to your concerns, they may be more likely to ask for assurances from the company providing the service.
The main thing I would suggest is that your Power Feeder is protected with a good Transient Voltage Surge Suppressor ("TVSS"). This is good practice anyway, and this kind of protection might already be installed, but if not, this would be a good time to add it. The specific type and size is dependent on the characteristics of the power plant being protected, so I would suggest that you consult an electrical engineer familiar with the specifics of your building power. This is about all you can do, short of buying individual UPS's and putting them on your most critical pieces of equipment. If you do that, however, make sure you use true, "double-conversion" UPS's. The less expensive "line interactive" units can do funny things when connected to generators.
My biggest concern would be how the switchover to generator will occur. If the central UPS has full wrap-around bypass, this shouldn't be a problem. They will probably just get the generator running and switch the bypass to it. (Note the later sentences in this paragraph, however, regarding "sequence".) If the UPS has only internal maintenance bypass, then it sounds like they'll need to totally "down" power before switching to the generator. In that case, you would need to do an orderly shutdown of your data center, wait until any other loads are switched over, then start bringing your systems back up. You would probably need to do the same thing when the UPS is restored. The important thing is that full loads are not suddenly switched to the generator, which would most likely cause it to become a little bit unstable for several seconds when the load hits. You want your most critical equipment to be the last things switched over, particularly if this power shutdown will affect non-UPS equipment like building elevators or air conditioners. Those should definitely be brought online before any electronic equipment is switched over.