There is no set rule as to how many have to be from anesthesiologists. However, common sense would dictate that you should have at least one. Most programs require 3 letters and ERAS lets you submit up to 4. IMHO, it's the quality of the letters that matters more than the quantity. Try to obtain letters from big names or with direct connections to the programs you are interested in. Personally, I submitted 4 letters - one from an internal medicine attending and the other 3 from anesthesiology attendings, and I matched at my #1's for both transitional year and anesthesiology.
As for the school, coming from a big name school looks nice on your resume. This is just speculation, but I do believe coming from a well-known med school helps you more than coming from a mediocre school.
But it's also important to have additional credentials like good board scores, letters, interview, etc. Does ths mean that if you graduate from Harvard you are guaranteed a residency spot there? Of course not, but all else being equal, I'm sure they would give you preference over someone from a no-name school. On the flipside, that someone from the no-name school has a better chance of matching at their program, and even at Harvard if they have connections or did an away elective there.
Just take Step 2 and rock it - that and the letters are the two most important things you can do to bolster your application.