Does it sound like she likes me?

Aside from obvious body language and other "Signs," I'm pretty sure my crush might like me back.

She accepted my invite to a basketball game saying it was sweet of me to ask and that she would love to go.

Unfortunately, she had to cancel the date since her mother is making her go to her cousin's baby shower. She responded "Why did I know something like this would come up... I'm so sorry"

Sometimes she won't respond to my texts, other times she does and she keeps the conversation going with interest.

Does she like me or no?

It's really hard to tell, but don't bombard her with text messages. If you seem needy or obsessive, it's usually a huge turn off.

It sounds like she likes you, but I agree with the poster above. Make sure you aren't bombarding her with messages and cut her a little leeway.It sounds like she likes you but still may be a little more unsure. Show a little more confidence to her, that should help. Good luck!

I'm like this sometimes, usually i'm just too busy and until I really get to know a guy I won't put aside too much time for them, once I know that I like him I'm usually all ears though. Give her some time I'd say

When I get messages from whom I have a crush on, I would try to answer them however busy I am. But it's for me, so take this as an example.
What are other "signs"?

I agree with shicchan. When I get a text from my crush, I respond even when I'm busy. But it really depends on the individual too. So, she might or might not like you. I don't think you can be that sure. Anyway, good luck :)