Question about External Hard Drive (HDD)

I have a laptop with limited storage and I am planning to buy an external hard drive just for storing some of my games. I don’t plan to play games directly from the drive. I just want to copy and paste them onto it to free up space on my internal SSD. Later, when I want to play those games again, I’ll copy them back to the SSD. I have really slow Wi-Fi, so redownloading games isn't a good option.

My questions are:

Will the games still work fine after copying them back?

Will doing this kind of copying damage my SSD over time?

Thanks in advance!