Can I install on demand games to a USB drive and play them from it?

Yes, you can. I have most of my GoD games currently on USB Flash drives and they work with no issues.

I would try this if you have two USB drives now. Install the install disc content on one USB drive. Then install the Play Disc on the other USB drive. Now the game is pulling data from the USB drives completely and you should see an improvement.

Try getting a usb drive, format it on the computer before using it on the console. Then move the other GTA5 files to the usb drive or to the Cloud and delete them from the hard drive. See if you can install the game then.

Under settings > storage options the discs show as separate items from the save files so you should be able to delete disc 2. Rockstar designed GTAV to be installed on the hard drive which has faster access than USB. It would then load assets from the disc
one install on the HDD and from the disc 2 Play at the same time to load assets as fast as possible. A USB drive will work it's just not as fast and you will get longer load times and pretty severe texture and model pop in.

I honestly couldn't stand the game until I bought a USB drive to install the Play disc onto. That way disc one loaded assets from my HDD and the play disc installed onto USB drive. Benefit being while USB isn't as fast as the HDD it's a lot faster than the
disc drive and even better quiet.

The correct install is just disc one and disc 2 in the drive while playing.

As for saves you can create a copy of them. If they are on your USB drive copy them to the internal memory unit and vice versa if they are on the internal memory unit. You can also choose to back them up to the cloud with gold where your console will keep
a copy of the save on MS servers.

Yes, you can put Games On Demand (as well as Arcade Titles) onto external USB hard drives or flash drives. The biggest partition that can be used is 32 GB. I have run several Games On Demand off of USB flash drives and have had no performance issues.