It is possible but expensive.

But the kind of night trains I used to take, no. But that's because I was cheap.

I even took regular, non sleeper night trains. Sleeping on seats is not as good as on beds but much than on planes or buses. These tended to be really cheap.

One interesting thing they did in France was to run high speed trains at low speed through the night (iDNiGHT). The idea was to get an extra "free" slot. Really cheap (I think I paid something like 10€ for a ~900km trip) but not the most comfortable. Still managed to sleep. I liked these but few people did, so they cancelled the service.

I took a cheap sleeper train across Germany once and the sleeping surface was essentially unpadded. I don't know if this is normal- maybe everyone brings their own?- but sleeping on an upholstered plank (billed as a "couchette") did not make for a restful night. I don't think I slept at all.

The joke was that I had a sleeping pad with me, but I didn't dare try and dig it out of my pack in the dark cramped shared compartment.

Yes, couchettes are differ a bit in hardness, but not everyone can sleep on them (I can about half of the time); in other languages they're called "lying-down cars", as opposed to "sleeping cars", where you get a proper mattress. I've never seen someone use a sleeping pad on top, but you could definitely try; I have thought of doing that too but not tried it yet. It would be easier if you get on a bit earlier in the evening, or the starting station.

I usually use a thin (cotton/silk) sleeping bag because I can't be bothered with the provided linens. No sleeping pad, and I don't think I've ever seen anyone use one. I think the padding is fine, it's certainly not unpadded. The more expensive compartments do have more comfortable beds.

It’s not that expensive, we had a private cabin going Florence - Munich for about the same price as a hotel night. That was with a shared bathroom but we had a sink in the room.

Certainly that's the case on the London-Scotland sleepers.

Yes I took a night train trip from Vienna to (I think) Göttingen (final destination was Kassel) last year and was able to have a single compartment with bathroom all for myself. It was pricey but not pricier than a flight from Vienna to Frankfurt and then a train from there to Kassel, because low-cost airlines don't fly this route.

Yes, if you can afford it.

Why do you need that? Are you alone when you travel in a plane?

I'm alone in a hotel room. That was the frame of reference.

only downside, very few have double beds. (Only twin beds with one over the other).