Going to be doing OoA adventure path and looking thru the google I found an neat idea a Power Armor Inventor with Wrestler dedication, any suggestions on ancestry fleshwarp might be interesting and thematic. In Alkenstar magic does not work right? If so how would that effect creatures like Automatons?
I recommend you get the OoA Player's Guide from this site, since it answers quite a few of your questions and has some good advice.
The short answer though is that the AP assumes magic works normally for the AP, just so no class gets penalized. Fleshwarp is a very neat ancestry but it's also Rare so you'd need to ask your GM if it's ok (but, given Alkenstar's proximity to Nex, I think it'd be fine).
I'd like to do a Barbarian but I don't like any of the OoA backgrounds. IS there a problem for the GM if none of the players choose any of the backgrounds with there adventure hooks?
No. You'll be fine without it.