Does a third party fixing my Mac have access to my files? My old Macbook kept flashing between a prohibitory symbol and a folder with a question mark. Internet recovery stopped working when I tried to use reinstall Sierra OS, so I initially gave up on fixing it. Now, someone I don't really know is going to try fixing it for me.

If possible, I'd like to know if they'd have to access/search my files to fix the issue? I'm a bit of a private person, so I'd like to know what's going to happen. Would it be better to take it to an Apple store instead?
In order to repair a Mac you will (generally) need an administrative password as doing things like reinstalling software and the like requires an admin password.

Even if you create a separate admin account for this person to use in effecting repairs an unscrupulous person would have no trouble getting into your stuff.

Unless you have put your personal information inside an encrypted .DMG file. Then even if you do create an admin account just for the repair guy the chances of him getting to any of your personal stuff is practically nil.

So no they don't have to access your personal files to effect a fix and an honest tech would never do that. Hey if I have to give my Mac over to Apple for repairs I back up my profile and then delete it and create a temporary profile for them to use, just in case.

But if you can't back it up then your next best thing is to put your stuff in an encrypted DMG for the duration and pray there is no data loss. Also pray that your tech is a scrupulous, ethical, person. Regardless, at that point, there is little or nothing to see anyway.

I learned a long time ago in the IT biz, the stuff on most people's computers is uninteresting to everyone but the owner. And that combined with ethics keeps me out of other people's stuff. be sure you trust whoever looks at your Mac.