Advice. Does she like me?

So I’ve been talking to this girl over snapchat for a while but we have spoken a lot over the last month and now I fancy her. Basically I’ve asked her to meet up but she said she only free in a months time. So I need some advice

1) I didn’t explicitly state that I wanted to go out with her on a date but it was pretty much implied by my message that I sent her on NYE. Is it bad that she said she’s busy and can only meet up a month from now?

2) she gave me her number. Is it better if I text her rather than using snapchat photos?

3) she used to pretty much initiate all the snapchat convos but recently has not done this at all. I imitate a convo with her every 2-3 days and when I do she seems really interested we talk a lot and there is a lot of reading and jokes. Is this bad?

Basically I just need some advice on all of this. Thanks.