none of it really counts. What really counts is your skills and ability to confidently talk about them. Or put differently, its your choice if internship or whatever experience really counts. You also have to convince the prospective employer to respect your choice, but if you can confidently represent yourself that may be easier than you think.
Definitely. It's all about learning a lot and then speaking with the confidence and ability of someone who knows what they're doing and comes across as able to learn more.