Congrats on the internship! You're heading in the right direction for federal service.
So I can't speak on the summer internship aspect. I was offered a pathways position (it was full time) once and I had to work 2 full years to get my competitive status and then in my third year depending on funds and such I'd get the permanent status. It wasn't an automatic conversion if I remember correctly (I ended up turning it down cause it wasn't in the agency/field I was interested in, so my memory is slightly foggy on it) I'm gonna say you don't get an automatic conversion if it's just for the summer. Definitely ask HR on that though.
Since it's an internship you probably won't get benefits. But know that if you were to get a temporary position (like a 1039), you would. I worked a seasonal position and was offered benefits. I didn't take it because I was still under my parents insurance and we made the decision to keep me on till I got a magical permanent job or I got kicked off. Technically you're not getting paid more, you just won't have money taken out of your paycheck. When I was at my seasonal position, I had money taken out for my rent (they gave me housing) each month, but my colleague had money for rent and medical taken out, so my paycheck was a little bigger.
Never hurts to ask about pay. I would say you might be able to negotiate your step for sure. Worst they can say is no.
Top tip: SAVE YOUR SF-50. This will be helpful when applying for future government jobs.