I was wondering if you can put feats on the Big Fig sinistro

Sure, nothing in his rules says he cannot be assigned feats as far as I know.
The only exceptions are Shellhead and Lazarus Pit, which cannot be assigned to any Colossal.

So a different question, with nanobots, could you start sinistro at his 100 point dial then nanobot up to his 200 point dial?

No. A figure can never heal beyond its starting click.