1. All sound natural. The choice between movies, cinema, and pictures really depends on the cultural preferences where you are and who you are speaking to.
2.heart to heart - a serious discussion involving your emotions as well as facts and figures!
3.He suggests that we should put our relationship on hold.
-“Put something on hold” means “postpone or delay something”, right? - yes, here it means that he wants them to stop seeing each other for a little while, or to stop progressing the relationship
4.He does not want to burden anyone with his troubles.
-This means “ he doesn’t want to make anyone a burden with his troubles”, right? He doesn't want his problems to become someone elses worries
5.What does “Jambalaya” mean?
It's a spicy Cajun stew (American)
6.– He does not want to put me through more troubles.
-This means “ he doesn’t want to make me incur or bear more troubles”, right? yes