Why do you think the movie felt awkward? Who did what, what kind of awkwardness, how did you know, please elaborate.

Bold part: framing the question that puts her on the spot doesn't sound good to me; instead of asking her to admit her feelings, consider expressing your own instead:
1. You can control how you want to express -- your relationship is still in early stages, so a straight out I LOVE YOU would be too heavy for an almost-stranger to take. Typically something like "I am interested to get to know you better as a woman" is already very clear that you're invested, and it doesn't force them to respond another heavy one like "I LOVE YOU TOO".
2. You put yourself on a vulnerable spot and that takes courage, generally ladies would appreciate that.
3. You learn to take rejections... Process and reflect then move on, so you can build your confidence with each rejection, along the lines of, "I've been through worse, this is nothing" or "ah this sucks, but I've tried"

HOWEVER, all this is definitely big no no if you're convinced things are awkward right now -- everything has timing... Any interest she has towards you can be instantly thrown out of the window if you do it wrong.

Hey no worries. Sounds like the awkwardness wasn't really a big deal, I think it's fine to just admit the movie date didn't go well, can even joke about how bad it was and all. If she's receptive of your chat then you can ask for another try at lunch date or something, find somewhere cozy where you can talk and chill.

As for breaking physical barrier: personally for me, I'm slow to warm up so too early would likely scare me away. I'm sure there's a spectrum and I might be on a far end, you'll just have to find that out what may work for her by observing her in person. If she touches you herself then I think that's a positive sign.

Ahh, small "accidental" gestures are fine. What I had in my mind was an incident where I met someone I barely knew at a public function, we sat down and talked, and he proceeded to touch my thigh like holding for way too many seconds, and it was very uncomfortable to me. I was frozen in fear in that moment, but it's been so long, so it's not something I'd make a fuss anymore.. just that the fear is etched in my mind.

To many, I may be overreacting for a simple touch like that... But I wouldn't want any awkward sincere guy looking for love to be mistakenly taken for a pervert lol. So just saying this that if you wanna create accidental touches, that's fine until she realises you're faking it. If you're too nervous to be natural, then it means you yourself aren't ready to break the barrier.

"How are you" is a terrible question to a stranger because if I (as the recipient) know it's a courtesy question from you, and I don't care about you (yet).

Honestly, I don't ask that question to a friend on text chat. Even in person, I'd ask if I haven't met that person in a while but for a stranger, I'd say there are better things to ask. I think, for someone to be on dating app, chances are the person isn't having a shitty life (at least free enough to care about looking for a partner) -- you won't be getting any plot twist level of answer.