We heavily use LogMeIn Rescue where I work (it's a legitimate program, but you have to make sure the person behind it is legitimate), so I can tell you exactly what we have control of.
Yes, they can see all files if you give them permission to the File Manager. Once connected (after you download and run the Rescue applet from logmein123.com), there's a few different prompts that can come up, and basically determine what you gave them access to.
Usually I go for UAC access first, which will prompt you about the technician wanting admin access. At this point, your Windows Firewall may also popup to allow the executable to reach out to the network, where it makes the peer-to-peer connection. If you allow it, then you get a UAC prompt to accept to give the program full admin - at this point, I (they) have full control and access to about anything. You usually will still see prompts for each "module" though. This whole part is optional, but really makes things smoother; for example, without this step, I can't see UAC prompts if you run a program as admin, the screen will just freeze until you click it on your end.
The remote control itself is another step, which can be done with or without the previous step. It will give you a prompt like "Technician would like to view and share control of your desktop"; accepting this gives me (them) full remote control of your mouse and keyboard. At any point, you still have control, and can kick me out with Break, or fighting the mouse and closing the window quickly.
A separate prompt comes up for File Manager, and once allowed, I can see all drives on your computer. I'm not sure if permissions apply if you didn't give them the UAC admin, I've never tried it since I always get admin first. I can just read and write any file on your computer. When a file is transferred to or from your computer, the main window with the chat will show it, along with a progress bar of the transfer, so it's easy to see if they did anything. I'm not sure where this is logged, pretty sure it is saved somewhere.
So bottom line; yes, they can see everything if you let them.
To make sure they cannot get back in, just close the window or hit the red X, it will prompt you to terminate the connection. The other thing to look out for is the Unattended feature; this let's the technician remote back into the system at any time, but it usually is for a set amount of time. You would be prompted for this, and it would ask for your Windows password so they can log back in automatically if the system is rebooted or logged out. This feature usually shows as a blue circle icon in your tray by the clock.
Also check installed programs for anything LMI related.
I'm guessing you had a remote scammer as well. If it came from a website stating you had a virus and to call or connect to them, or received an unsolicited phone call claiming the same, it is 100% a scam.
Edited by Demonslay335, 04 August 2017 - 06:23 PM.