Yes, you can change the install location via Origin.
- If you want to change where the game gets installed do this:
1. Click on the Origin Menu (upper left corner of the client)
2. Select Application Settings > Install & Saves tab
3. In the On your Computer location of this tab, you can change the location that the game gets installed.
2. Maybe, depends on if step 1 doesn't work, but step 1 should work.
3. No you won't loose your Sims 4 folder if you back it up first. - Basically back up your Sims 4 folder to a USB drive. This will make sure you won't loose any saves or anything in the Mods or Tray folders.
4. There shouldn't be anything else to consider. It should be pretty simple to change the install location via Origin with the photos above.