I changed my PS3 hard drive to 500 GB three days ago, and unless you know exactly what you are doing (Formatting the external hard drive for the backup, restoring the ps3, etc) then I would expect to have problems. It is not as easy as the "How to upgrade your PS3 HDD) websites and videos make it seem. As long as you have your save data files safely in multiple locations such as flash drives, you don't have to worry about too much. Expect to have problems if you are upgrading your HDD.
You cannot play a digital game unless it is on the PS3's internal drive. You can't play it from an external drive. External drive would be useful only to back up game utility data, save data, and other files.
If you upgrade your HDD, make sure you have the external hard drive formatted so the PS3 can read it. Otherwise it will not restore the backup. That's what happened to me, and I had to download everything all over again. Luckily, I had all my save data on PS+, so I didn't lose it.
Been away for a bit, but sneaking back in.
Gaming on: PS4, PC, 3DS. Got a Switch! Mainly to play Smash