I have unknowingly installed the "play" disc of GTA V on my Xbox 360. Although I'm not noticing any lags just yet, I'm worried about the reports of bugs and slower frame rate. Is there a way to delete only the 2nd disc of the game? And if not, would wiping out the game completely also wipe out all of my saves and settings?
It won't wipe out your saves as long as you delete only the installed disc. The process to do so is:
Go to Settings > System > Storage > Select the Drive it's on > Games and Apps > Find GTA V. Select it.
Under there you should see the different items separated out including each saved game. Disc 2 install will probably be a single item Listed as Installed Xbox 360 game. The install that runs for Disc 1 breaks it up into 4 different parts.
Select the Disc 2 install with A, and then you'll have an option to Delete it.
I would check the storage for your game data. If you go the the Settings tab on the far right go System > Storage > (Hard Drive - assuming you are using the hard drive) > Games and Apps > (Grand Theft Auto 5 - may be "GTA V" or something, but it'll be straightforward enough). Although it may depend on how GTA 5 manages its data, you should see something like "GTA V" with a subtitle like "Installed Xbox 360 Game" and is likely taking up lots of space (in the GB range). I don't know enough about GTA 5's disc setup and such, but I think that should get you where you want. Simply select the item you want and hit Delete. (I based some of this based on my Xbox and my Skyrim disc install, so, again, it may vary)
Hope this helps :)