1,This is when I first registered at the cultural center.
2,We had an awkward but interesting conversation because we met by common interests.
3,We had a lecture about painting and had an interesting conversation.
Here's your corrected homework, Ms. Jane. Please go over the revisions given below.
Have a good night's sleep and see you tomorrow! 
Cheers,
Jean~~
1. This is when I first registered at the cultural center.
>>> This was the moment I first registered at the cultural center.
>>> OR: This was when I officially registered at the cultural center for the first time.
2. We had an awkward but interesting conversation because we met by common interests.
>>> We had an awkward yet interesting conversation, sparked by our shared interests.
>>> OR: We ended up having an awkward but fascinating conversation, thanks to our mutual interests.
3. We had a lecture about painting and had an interesting conversation.
>>> We listened to a lecture about painting and had an insightful talk afterward.
>>> OR: We attended a lecture on painting and ended up having a lively discussion afterward.