Question: I'm new here and I saw one can buy them e.g. in Germany at bitcoin.de via an online transaction, by paying Euros. Is the same possible in Romania (do you need a €-bank account for that?) and if so, is there some (online) exchange service best suited for that?

Answer: 
You can check out a list of exchanges that accept customers from Romania over here: <https://bitcoinnews.ro/cumpara-bitcoin> 

If I remember correctly there's one international exchange that accepts RON as well and that's LakeBTC. I haven't seen any reviews of it though so use with caution.
See if [bitstamp](https://bitstamp.net) or [kraken](https://www.kraken.com) work for you. Both accept SEPA transfers. There are also some other European exchanges listed [here](https://bitcoin.org/en/exchanges).