Similar situation as OP. A group of us went out to dinner, I asked her to go to a luxury theater with me in person. Made the plans via text. We had a 1.5 month dalliance (no sex) over the summer. We still see each other almost daily.
Do it however you are most comfortable. If you see her and feel like asking her out right then and there then go for it. Maybe she might not be around or you are both busy during the day you would ask so ask her via text.
You can do that. I mean she was content with just chatting to you through messenger. If it were me though I'd find a way to ask her verbally because in my mind it feels more natural and comes off as more confident. Since you have her number what's stopping you from popping the question through voice?
It can be done, but in another situation might be better if possible, though context can mean a lot.
I actually asked out this person I've been with for a while now day after a New Years had gone by. She was texting me and I was texting her, and we had been hitting it off after chatting for over a year at the time, but she was dead-set on achieving a goal in school for her future and though she had dated before, she had never really been to close to anyone like that and hadn't gone very far in any sort of relationship and broke it off with them, and at the time over the last several months I had realized I liked her (I have a history of dating too and know more about myself in this area because of it), but she was apprehensive to really letting herself come to like someone. Viewed herself more as someone who wasn't really one for relationships from her past experiences. She was just telling me over text since winter break was ending her studies would keep her busy, we might not be able to talk or hang much, it was kind of half-hearted but I did sense what was going on. I decided if I didn't say anything now, she was probably going to slip away from me, and I didn't want it to come to that, so right then and there I just bluntly told her what was on my mind, how I felt for her, and she didn't need to return the feelings or feel she needed to answer me, but I just couldn't let things slip by and end like this.
In retrospective, I am very glad I did that, she is used to taking on things herself and focusing in her studies and work, and to most she can seem emotionless at times, but she's a deep-feeler and contracts a lot of it in herself, but she's opened up a lot more with me over the time we've been dating. When I asked her out, she called me and we talked for a while, she was in tears at the time. The texting made sense in that moment to confess rather than call to do it, I realized she was processing things and trying to decide where she wanted to go with her life, and maybe it was selfish of me to spring that on her, but I don't regret it at all, even if it didn't work out.
While asking someone out by text isn't 'optimal', it definitely can work, I guess depending on your guy's relationship and situation.
dick pic might be the only possible way that he screws it up at this point.
"asking her out" is just a formality. He clearly wants this girl to be a bigger part of his life, she feels the same way based off what he said, these things should just work out naturally. Yes, even for someone who has to check with GAF first. Get her to a movie/dinner whatever and just let biology do its thing.