making patches

Is is possible to make patches for a stand alone application?
EX: If I make an application that runs off of a usb flash drive will it be able to be updated?

I would investigate Patch Maker, assuming you can still get it from Clickteam.
You can deliver patch for your applications by internet or however you want then.
Unless your application is huge, I wouldn't bother personally though.

I know you can make patches for software installed on a system using the patchmaker.
I'm wondering if the file is a standlone application and not installed on a computer, whether or not a patch can be made.

Well, I would certainly think so.
It just takes two files at one end; your original and your updated executable. Then it generates a third file that bridges the gap.
That's my understanding of it anyway. So it should surely work for standalones on that basis.

Sure, it's easy to write an auto-updater. Use the Get object to check an small text file on a server which contains the size/checksum of the current version, then get any old versions to download to Apppath$, then generate a batch file with a delete old & rename download to new & a run new command, and run the batch file before quitting the old version.
If the batch file runs before the application has completely closed, the batch file will fail, but you can work around that.