New guy creeping me out

So there’s this guy from an online dating app who I just met about a week ago. He’s very excited and apparently very serious about me. We met in public and sat in my car for hours talking and he began to start saying things like “I feel we have a strong connection” and was gently rubbing my hand trying to kiss me on that same day. I thought it was sweet but awkward at the same time. Mind you before we even meet he tells me that he can be awkward at times. One day after meeting with him in public he sends me a text asking “did you slept well last night?” and not long after that I got an email via text from him saying the same exact phrase. He does have an iPhone. I know it was dumb of me to do, but I invited him over a night when we were supposed to go to the movies in public, but he got off late and I was tired anyway. This was only the second time we met physically. He’s been saying a lot of sweet things to me and it’s sometimes overwhelming like I don’t believe it or there’s a weird vibe I get or some type of manipulation he’s spelling on me. Here we are at the beginning of this new week and I’m starting to feel uncomfortable about this whole thing. Considering the email text, do you think this could be a dire situation as in him being a stalker or worse?

Update: he also has a history of suicidal depression

Update: I’ve tried to have a talk through text to tell him that we won’t work and he’s asking me why there is a sudden change.. he’s upset and cursing at me and voiced to me that he doesn’t want me to be another again.. I’m nervous 😥😓

Update: everything is much better today yesterday I just stopped texting him after three hours of getting nowhere