Recent Engineering Graduate with Questions

Hi, I'm a recent graduate in electrical engineering from UCSD, my UC GPA was 2.99 but I have an overall GPA of 3.44 (this includes my community college work). I'm finishing up my first year working as a full-time engineer but am thinking about switching into investment banking. Got the idea since my job entails a lot of excel work and keep hearing about IBanking.

1) Is it possible to get an analyst position by just cold calling and trying to get an interview with a revised resume?
I'm in Silicon Valley I heard that boutiques could be my best chance.

Otherwise I think my best option would be to do a full time MBA. I'm in the bay area and was looking at Stanford, Berkeley, with other choices like UCLA, University of Austin, etc.

2) What are my chances of getting into one of these schools given my academic history (assuming good gmat scores)?
I know a top tier school is highly recommended (does this include the top 25, 30, 40?)

3) If I must get an MBA from a top school, could I come in as an associate? Otherwise would they hire me as an analyst considering my age and 1 year experience? (I'm almost 26 I'd be 29 by the time I got my MBA).

4) Also trying to make my way back to San Diego eventually, are there jobs there in this field?

Thanks!