Always go for a single reputed SEO firm, don't do SEO from different firms.
No you CANNOT do too much SEO
It is always best to start slow and measure your success which you can always scale at a later date. Doing too much when not needed could be counter productive.
Definitely Yes! Google especially has been making great moves over the past few years on websites that are using too much SEO to manipulate rankings. Getting thousands of backlinks in a few months isn't a natural type of linking. I suggest that you do it in moderation and make it as natural as possible.