Questions: Dating

Say, I have asked a girl out and she said no. Should I chase after her or let it go?

Me and my girlfriend are doing long distance relationship. She moved to another country for her dream job. Our relationship is realy great except one fact. She likes to meet new guys. She dances with them in the club, talk to them and share her IG account. All the time she says that it doesn’t matter and she is not responding to them but for me it is unacceptable. We spoke about it and she told me that she will not change that. That she likes to meet new people, she is feeling alone in that country and she will not change her rules. Few times I asked her if she met someone. She said no... and it was a lie... I don't won't to control her or lock i na cage. She can do whatever she wants... chatting is ok... but not telling that she has a boyfriend, dancing and giving IG is to far for me. I had an idea, that If she want's to live like that she should post our together photo on IG. Guess what? She will not - it's another rule. I trust her... but not everything in life is about trust. I’m one step from letting her go… We are not so young... she is 30, and I'm 36.

https://www.girlschase.com/content/what-backward-rationalization-and-how-it-affects-you-girls

detail story:

a guy is in holiday trip to japan , he is at osaka , then he tried bumble to get a date , later he get one

so they hang out at bar for drinks , the girl only drink one glass , it went really awkward because she can't speak English and the guy can't speak japanese , they communicate using translator app like 99% of the time.

things getting better after they left the bar , they just walk around osaka while holding hands , later he offered if she wants him to walk her home , and she said yes

then he ended up being in girl apartment , they just sit there and continue awkward convo with translator app , the guy love dog and he playin with her dogs for a bit , then after around 1 hour he decided to leave , he is not sure about what is goin on because the translatore is not so good , sometimes it didn't make any sense.

please vote , thanks !