Log shipping confusion
1) Is that the correct code to run?


Well, kind of. It would probably look a bit more like this:

RESTORE DATABASE [YourMom] WITH RECOVERY



  2) Does that automatically restore any transaction logs that have shipped since the last restore Agent Job was ran?


No, it's your job to make sure that Log Shipping is caught up, and if possible (if the primary is still available), take a Tail of the Log (sounds like a bar, I know) backup, which will grab any remaining transactions, and put the database on the primary in a restoring state (will cut off any current users). The TOL backup is a usually a manual step, unless you have third party tools (like Quest LiteSpeed to help).


  3) Once the restore Agent Job runs, do I need to keep the .trn files?


This isn't a yes or no question. You should keep all backups according to your data retention policy.

Hope this helps!