I think your F3 is fine. The mirror can be lifted without harm. If you had used the brush attachment, I don't think it would have had a good enough seal to generate enough suction to lift the mirror.
I have used a vacuum to pull a stubborn hair off a mirror and focusing screen. I used a bulb blower with a short length of hose attached. When releasing the bulb after squeezing, a vacuum is produced which is sufficient to remove individual hairs and dust specks from inside a camera, and the soft tubing won't harm the mirror or screen. To be extra careful, you can cut the end of the hose so it is a bit rounded instead of straight, so the entire tubing end cannot be in contact with a surface at any time.
Cleaning mirrors is definitely a source of controversy. Specks mean nothing-they will not degrade the viewfinder image, unless they are more like a coating of dust. From shooting in desert places where the wind is almost constant, all my cameras have at times gotten a fair amount of dust on their insides. Anything painted I swab with a moistened Q-Tip or rolled-up moistened Kimwipe, rather than just blow it around. For mirrors, I hold the camera body with the lens mount down and blow with a bulb blower, angling to avoid blowing it onto the focusing screen. The F3 is easy, because the mirror can be approached through the top of the camera by removing the prism and focusing screen. Stubborn dust usually comes off with careful use of the bulb blower as described above to create a vacuum.
For actual cleaning of a mirror, which I have done after years of use, and once after a friend's kid touched a mirror while I was showing his dad how to change lenses on pre-Ai Nikons- it's best to let a technician do it, unless you are the type who is careful enough and patient enough to do it properly.
I have cleaned my own without any problems, but I wouldn't advise just anyone to do it.. I use a Q-tip, fairly damp with lens cleaner, to float off any hard particles. The fibers will catch and pull off stuck particles. After two passes, I follow with a lightly moistened rolled up lens tissue with the end torn off to create a soft edge.
A couple things to remember: just as some specks on a mirror will not cause a problem, a scratch will not mean it is unusable. So a scratch from improper cleaning is not a disaster. But just as with lenses, better a layer of dust than a web of fine scratches.
Something I've wondered about:
I acquired a Pentax MX a while back which had a cheap crappy zoom on it with a loose aperture lever- so loose it had come out the back of the lens and was in contact with the mirror. I managed to get the lever to come out of contact with the mirror by taking the lens apart, after the failure of judicious use of Newtonian physics (i.e., tilt the camera toward the floor so the lever could be dislodged by gravity and gentle shaking fore and aft on the lens axis, followed by gentle smacks on the back when that didn't work).
When I got the lever out and the lens off, I looked at the mirror. It did not have any scratches or marks whatsoever, even though the lever had been jammed against it and had tilted and run along the surface for a centimeter or so.
I'm wondering if Pentax had put a hard coating, like lens coating, on the mirror. If the mirror were silvered, as opposed to aluminized, such a coating would be necessary to prevent oxidation.