2) Basically, noise rules tend to vary by commune. But in practice, you can raise merry hell from 7:00 to 22:00 without fear from Monday to Saturday, and you should expect complaints on a Sunday or out of hours.
If whatever DIY you are doing does not involve noise, then no restrictions whatsoever.
3) Almost certainly not. It would be polite to tell the neighbors that work is scheduled, but unless there's something in a contract somewhere that you already know about (you are after all the landlord AND syndic...)
4) I guess the work you need to do is so you can rent out the last bit of the property? Sure - delay it for 2 months for your tenant with exams. But only if they agree to pay for the extra 2 months that the property will be void. But get something like that in a binding contract.