I bought 2nd hand an old carbon framed mountain bike and from the emblem I believe it to be Giant make.

I want to turn it into a single speed and it looks like the rear dropout and hanger are combined and replaceable. Photo attached.

Does anyone know if I could get a replacement part with a horizontal dropout setup?

Also, does any suggestions on how I could find more info on the frame? Its been repainted and I can't find any markings anywhere.
Thanks

I don't think horizontal replacements would be available. But, if both sides bolt on the same way, you could fab up a pair yourself. You'd just need a drill, hacksaw, files...and plenty of time.
It would be easy to have a machine shop make some too, but that wouldn't be cheap- it would probably cost way more than the frame did.

Of course with a $20 chain tensioner you'd be ready to go in 10 minutes!

I'll agree with Live Wire. I would think that tabbing some up wouldn't be particularly difficult. Perhaps you could fine some weld-on dropouts that would have enough material to cut off the weld areas and shape/drill appropriately for your frame.

Find out where to get Fuji Track Pro replacement dropouts. There's probably a way to get these to bolt up:

Good idea, but the bolt pattern is slightly different, so expect to do some re-working.