Which date ? This night train should be available on tickets.oebb.at so please check there first : add Interrail as a discount and select one-way tickets. It may not be sold out as Interrail is somewhat unreliable...

There are 2 other night trains from Budapest to Bucharest : 15:10 and 19:10. Those cannot be booked online but it is possible to do so in most big train stations, at least in Germany, Switzerland and Austria = no need to wait until you arrive in Budapest.

8. August

Then the 22:45 is indeed full. There are spaces on the 15:10 and 19:10 trains.

Buy the reservation at a train station in Germany, Austria or when you arrive in Budapest.

The train at 15:10 still has space but it says that only a paper ticket is possible...
How long does it take until it is delivered?
Is it smarter to make in Budapest on the spot (seat reservation) or online? Today is Monday I leave on Saturday

Definitely do not order on interrail.eu. It probably won't arrive until Saturday and it's way too expensive anyway.

No need to wait until you arrive in Budapest, you could make it at any SBB ticket counter for example.

Can I reserve a seat at a ticket machine or do I have to go to a ticket counter? How much does a seat reservation cost at the SBB counter in Zurich?

No that's not possible.

Probably around CHF 5. But I'd take at least a couchette. They're not very expensive to Romania, €13.40 as you can see in your screenshot above, so SBB will charge around the same but then in CHF.