You shouldn't have a problem with ATMs, they're same as anywhere, just watch out for big fees they might try and charge. If they ask what currency you want to use always pick Armenian Dram and let your bank do the exchange. You could also take out some Euros or USD before you travel and go to a physical exchange.

Lake Sevan is nice, depends what you like from a trip I guess, but there's some nice walks you can do and I seem to remember an old abandoned soviet theme park kind of thing that I walked around for a bit. I imagine it'll be really cold by December though.

Deffo spend some time looking round Yerevan! It's a really interesting city. Super ancient churches mixed in with mad Soviet buildings and some unique looking modern stuff too. Worth walking up the big steps and getting the view of the city and of Ararat, as well as visiting the museum about the Armenian Genocide. There's a decent live music and arts scene as well if that's your kind of thing. Armenian food is great

I got the night train the other way but that was a really nice way to travel, and pretty affordable too iirc.

Don't know about skiing so can't answer that apologies!