How valuable is the data on this drive to you, and is it backed up? Considering that you have an SSD and you've decided to install games on it, I'm assuming that you understand that all data is stored on the hdd or the ssd. Right?
By all data I mean everything. Documents, music, pictures, videos, etc.
Please; do yourself a favor and buy yourself a new drive and copy the data off of it if the data holds any value and you haven't backed it up. Data recovery services can be incredibly expensive, and there's no promise that they can help you.
To answer your question about sectors: Logical sector damage can mean different things in different contexts, but I typically think of it being caused by data being half written to a drive when their is a sudden power cut to the computer. The drive has an internal mechanism to verify the integrity of data stored, and if it doesn't match what it expects to find, it will give an error to the OS which tells it that the data is unreadable. The OS will then write to the unreadable sector and the hdd will write data to the sector or remap it to a set of reserved sectors set aside by the manufacture. If it remaps, it's considered physical damage because the original place on the platters is broken/unwritable. Please, don't think of this as an invitation to try writing to broken sectors to see if the drive remaps the sectors. All the indirect signs you gave (PC freezing, etc) is screaming to me that your drive is truly failing at a physical level.