Pathfinder Core Rules wrote:
A simulacrum has no ability to
become more powerful. It cannot increase its level or abilities.
I find this annoying but otherwise unambiguous. I don't think I would be able to add spells to my spellbook and such. I think in the adventure The Mask of Diamond Tears, an illusionist made several simulacrums(simulacrae?) of himself that could use spellbooks written with his lower level spells, but nothing was said of the duplicates researching new spells.
I do think for simplicity's sake that healing should work fine with me, as well as Dominate-type spells and protections or buffs and things. This is just my opinion, though. I noticed the spell description doesn't say just what type of creature I am supposed to be, so one could assume I should be treated like a construct or the type of creature I'm made to resemble.
Since a method of healing is mentioned in the text, it could be meant that normal healing and magical healing doesn't apply to me. I'm ok with that, I guess.