Is there any problem with a full installation on a USB drive?
Will it work in most systems (including 64-bit)?
Yes.
Will the installation contain only the drivers needed for the computer used for the installation?
Ubuntu doesn't install specific drivers for each machine, it' has a full stack of drivers.
You can, and should, during the installation, mark the box "Installing propietary drivers"
I have install Lubuntu 16 and so far it works, on every machine I could try.
Advantages of a Persistent install
You can use the Persistent pendrive to install Ubuntu to another computer.
A Persistent install takes up less space on the pendrive.
You can reset the Persistent pendrive by overwriting the old casper-rw file with a new one.
The Persistent install to pendrive takes less time.
Slightly less wear on the drive.
Advantages of a Full install
You can update and upgrade a Full Install.
If you have problems or wish to modify, the solution is the same as with an internal install, (You can ask for help in forums).
No ugly startup / install screen.
Better security, you can encrypt a Full Install.
You can use proprietary drivers.
Hibernation works.
There is no 4GB casper-rw or 4GB home-rw persistence file size limitation.
Generally faster boot than Live or Persistent USBs.
No - You should be able to do this just fine. In fact, so long as you're booting it onto a 64 bit computer, you can use the 64 bit version. And so long as you're doing that, you may as well go ahead and use 18.04, instead.
The drawbacks to this are fairly obvious:
- you'll be limited to the size of the storage space on the USB drive
- it will boot/read/write only as fast as your USB port will let it.
Other than that, go for it. I actually keep an install on a keychain for "emergencies"