[21M] and [20M], what's the best way for me to convey this?

For some background, my partner and I have been together for a year. We've experienced our share of ups and downs, but overall, things have been good—except when it comes to communication. I've been cheated on in my previous long-term relationships, and I'm working on healing from that. I'm careful with my words and actions now because I know my issues aren’t a reflection of him. I always try to explain my feelings clearly during our conversations. The challenge is that he tends to shut down when we talk, making it feel like I'm speaking to a brick wall. I asked him early on about his communication skills, and he assured me he could communicate because I believe it’s crucial. However, it seems he struggles with it. Recently, he created a game where he points to someone and asks if I would date them. I find it amusing, but my response is always, “No, I’m dating you.” In contrast, his answers focus solely on physical appearances and never resonate with what I express during the game. He often says I should trust that he won't leave me, but some things raise concerns. For instance, he’s clicked on links to hookup sites and still has his exes favorited on social media. There was even a week-long vacation where we didn’t talk at all, and when I finally asked for a serious conversation, he got drunk and only talked about a fun bartender he met. Additionally, he identifies as bisexual but exclusively interacts with women, which leaves me feeling uncertain about where I stand in this relationship. I'm feeling a bit lost and would appreciate any advice on how to proceed.