There is good advice in this thread.
My perspective is a little different but perhaps might be useful. It has nothing to do with the cultural thing, although I think the culturally based comments are valid.
Y'all have been dating 6 months or so, correct? At first she was infatuated with you and willing to do whatever to please you and she was super excited about you, telling all her friends, buddies, etc. There is that rush of excitement that comes from infatuation. It is heady intoxicating stuff right? Well it wears off eventually. This is NOT a bad thing in and of itself.
The infatuation needs to burn off because until it does you can't get a real read on who she is and how she is going to behave for LTR. Love doesn't develop when infatuation is going on.
My two cents is that she is into you, you are just getting more of a day to day read on how she is really going to be going forward. This is a critical phase through which to hold frame in a firm stable non ass hole kind of way. I do think the drama texting is something to nip in the bud, and the fight about her changing plans (a legit issue I agree) was overblown. Do not go crazy making. Not good on your part in my opinion.
Some of her recent behavior seems to place less importance on y'all doing things together (the Sat. shift for example - I think the Yum Cha is no biggie) and that bears paying attention to. I think you are in a stage where you stay engaged but be observant of trends in her behavior...and do speak up if something irks you. Don't blow up. Just be steady and matter of fact.
As far as your ex Romanian? It (in my opinion) depends on your gf. Yes you can be friends with whoever you choose. I'm friends with one ex I dated some 25 years ago. Not super tight close friends but someone I enjoy who I can always pick right back up with. I see him infrequently but an occasional catch up is nice. If a my man is friends with an ex, I don't care as long as I trust him and he's up front about it, but many women are not OK with such things.
Why not take your gf to meet your friend and go do something together? Like you I'd weigh which has more value the known quantity of the friendship or the potential of the relationship? It comes down to trust on that one. Can she trust the nature of that friendship and does you seeing your Romanian friend place undue burden on her trust? I avoid people who are overly jealous. Being trustworthy is on you. Being jealous (or rather not being jealous) is on her.
But generally I think the bloom is off the rose a little bit. It's just a natural part of the process. This is when you find out if it has possible legs for the LTR. If she makes the effort for you, enjoys you sexually upon request, and is generally considerate and caring then she has a deepening emotional investment and this bodes well. She also works in a supportive giving profession which is a positive sign often times. You'll have to judge it going forward and keep being masculine.