1. After editing a picture, I click on 'apply adjustments' then 'process.' Where do I find the processed photo so I can publish it online or print?
Select your 'Library' tab (looks like an index card) and look for the 'Session Folders' tool tab. If it is collapsed, click on the triangle which points to the right to open it. Hover your mouse over the 'Outputs Folder' tab and you should see where that folder is, or right-mouse it and select 'Show Info' then look at the bottom of the panel. Another way to find where it is putting your output files is to go to the 'Output' tab on the main menu (looks like a gear) and look for the 'Output Naming' tool tab. If collapsed, uncollapse it and hover your mouse over the directory shown in the 'Output To' field (hovering gets you the entire path). It is possible that you have placed these tool tabs under different main menu tabs, but the Library and Output tabs are the most likely.
2. How do I get a photo to save after it's edited. Clearly what I'm doing (see above) isn't working.
You don't actually save. C1 is remembering all the actions needed to be done to your raw file to create the output file. If you want to do two or more different versions, you'll need to look into creating a new variant or cloning a variant.
3. Is there any way I can choose where to save an edited image to or will it go somewhere defaultly?
You can choose by modifying the paths in any number of spots, but I would highlight the 'Output Folder' in the main library 'Session Folders', right-mouse and choose 'New Output Folder'.
4. At one point while trying to save my image, I clicked on "move to selects folder." It didn't move. It seemed to completely disappear. I tried this with several photos, and it happened every time.
As above, find out where the selects folder is, you should find them there. If you select the selects folder in your 'Session Folders' tooltab, you should see the files you moved to the selects folder.