All "fixing" bad sectors does as mark them as bad so they don't get written on again. Any drive with enough bad sectors to cause boot errors is a drive I wouldn't trust to store recipes for making mud on. As far as the brand relevance of the test utility, for future reference, it doesn't matter with Seatools.
It works on all brands and all types of drives and honestly does a better job than any other mainstream utility I've used. Drive fitness should be fine though so if it says you have bad sectors you can try using it's repair tool but I'd definitely get my files backed up first because I've seen many drives that flat refused to ever work again after "repairs".
I would highly recommend you get a replacement drive asap and if your drive has a restore partition on it, try to copy it to the new drive so you can reinstall. If you have Windows installation media, like a disk, I'd just do a clean install to the new drive as trying to clone the damaged OS to the new drive is likely to carry the errors with it. In any case, make sure to get your data and settings backed up from you current installation if you can.