Installing will just improve texture quality on most objects, decrease the texture quality on some NPC outfits, and decrease load times.
Installing has more pros than cons, so I would say to install it.
The only way to fix the bugs is to mod it.
Get
this program, and then follow this after putting your Skyrim save onto your USB, and then proceeding to plug it into your computer:
-Drag the Xbox Skyrim file into the main area of Horizon (the .exs)
-Go to "Contents" and extract Savegame.dat
-Change the extension to .ess
-Put the new .ess into the Skyrim save folder (My Docs > My Games > Skyrim > Saves)
-Load Skyrim PC, mod, then save as new
-Find the new save within your Skyrim PC Save folder, and move it to the desktop for easy access
-Rename it to Savegame.dat
-Now in Horizon, go back to the Content tab of the Xbox Save
-Replace the Savegame.dat within the Xbox save with the Savegame.dat that was a PC save
-Then click "Save, Rehash, and Resign" and you are done
(this actually only takes about 1 minute of actual work, not counting the modding because that depends on what you are doing)
You can then use the console commands to move Galum-Ei and Aela (or resurrect if you need to) to you, and do anything else.
Also this requires Skyrim for the PC (I am using a POS laptop, and have to run Skyrim on lowest settings, but it works as a mod tool), and you can get that from sites like Pirate Bay.
Honestly, if you bought the game already for the Xbox then why would you pay for it again? That would just be dumb (no offense to anyone that did purchase it twice for some strange reason).