Question about external hard drives

I have a 256 gb internal solid state drive on my pc. It is getting full. Can i just plug in a external hard drive to my usb 3.0 and just use it for backing up steam games?

yes. But if you plan playing games from the USB prepare for terrible loading times and some games that require fast hard disk access will be plagued with stuttering if you play them from USB

If you are just gonna store them there just to save you the time to redownload them the next time you want to play them yes. But if you wanna play them again you're better off buying an internal hdd or else face bad load times or added stutering in dynamical disk accesing games. On your SSD you should just have things you will use constantly and for a while, try not to constantly change things on a whim.

I play on it all the time, no problem. Not much noticeable lag and this is usb 2.

USB 3.0, assuming both the drive and your motherboard has it, should act almost identically to an internal hard drive in terms of performance.