Yes

Yes, provided the company accepts passes. Plus that it may in many cases not be very easy to even make that REServation. There will always be a sometimes quite hefty supplement to pay, for a real sleeper often equal or even more as a cheapish hotelroom. The actual nr of overnighttrains is not that high, most are in fact INland in some countries. There is also a difference between a real sleeper, with proper bed, or couchette, more like a lie down bench. Read seat61.com for more info on this. Due to covid some railways also have more strict rules now for sharing compartments as was usual.

If you have a pass with traveldays: the day of departure counts, so on that day you can also make other trips before you take that nighttrain. But if you need to connect next day to final destination, then you need to activate new travelday.

Depends on the Nighttrain
Nightjets (the Nighttrain brand of Austrian rail) accept 2nd Class passes in all Nighttrain comfort levels

In other Countries you need for the “deluxe sleeper” or a private Single Sleeper compartment a 1st class pass :)

Which Nighttrains to you have in mind?

From Venice to Paris. I am not sure which night train should I be looking for

From Venice to Paris there are no night trains

I am affraid but the Thello Nighttrain Venice - Paris is since 2020 not in service anymore and won´t be return in the near future as even the Brand of “Thello” stoped to exist :/

Your options is depending on the day of travel to catch the Vienna - Paris Nighttrain in Vienna or Munich from Venice. But as the Nighttrain Vienna - Paris operate only 3times per week it depends if it´s on one of your prefered day.

Option B. Is Nighttrain Venice - Munich and then with a 2nd travelday on the TGV from Munich to Paris :)