I would say that yes, it’s likely normal considering you pointed out that even though she is fluent in English, she isn’t well written. Perhaps she realizes this about herself and texting is a source of insecurity for her. If that is the case, I can assure you that she is spending more time analyzing her OWN behavior and response than she is thinking about how much time has passed since she responded. Secondly, how do you handle it? You don’t. Be patient with her. She’ll respond when she can. If you feel texting is really getting in the way of healthy communication, you do have her phone number and she indeed has a phone – pick it up and call her. A lot easier and much less confusing for everyone involved.
Texting her to meet up with you is pretty straightforward. You want to initiate a conversation before just asking if she wants to hang out with you. You want to text her, get a couple of texts going back and forth, and then text her about meeting up. For the first text with a girl, you want whenever possible to bring back what’s known in the dating world as “callback humor.”

Minor things like punctuation are not as important as the spelling itself. If you’re trying to “speak” a certain way and you want to emphasize something, it’s okay to use three or four exclamation points. If she doesn’t use any punctuation at the end of her sentences, then you don’t really have to use it either. It’s not really a factor at all. At the end of the day, it really all comes down to the way she texts and the way you mirror that.
Flirting to some is almost like an art! No matter how hard some people try, they really can't flirt for nuts whereas for some, it's really natural and comes with ease! For those too chicken to flirt openly, text messages are a great way to ask someone out for a date and get the message across without really worrying about being insulted! Therefore, I have a compilation of some flirty text messages you can use to impress that special someone. This SMS collection would surely inspire you to write your own poetic verses!