uninstall Adobe Reader?

This should do it:

http://www.ehow.com/how_6245350_uninstall-reader-mac-os-x.html

Note: in Step 1, they mean locate the Adobe Reader in the Applications folder in a Finder window (not in Launchpad).

I then read that it was for Mac OS x, less than the 10.7.3 operating system that we have on our iMac.

Like many vendors who state it that way, they mean OS X in general. You need to check the specifics of which versions of OS X it will run under. The version of the Reader you have/had, wouldn't even run under older versions of OS X.

That also is a point of confusion for many computer novices, or those who have switched to the Mac and don't quite get the numbering Apple used for OS X. Each point release is actually a major paid release, not just an update. So as an example, 10.3 was not free for users of 10.2. Apply the same all the way up to the current 10.8, Mountain Lion.

Anyway, the Reader will work just fine in your current version of OS X as it is the latest version of the Reader. Also, as people create PDF files with newer versions of Acrobat Pro, Apple's Preview is always behind since they have to figure out how to update Preview to properly display PDF files written in the new format, which also often involved new features. You will find that Preview will not always be able to display all PDFs properly, whereas the latest version of the Reader always can.

"install_flash_player_osx.dmg is in use"

Generally, the OS is telling you that the .dmg (any .dmg, which means Disk iMaGe) is still mounted on the desktop. When you double click a .dmg file, it puts a pseudo drive icon on the desktop. It's not physical drive like an external hard drive or other device, but the OS pretends it is. Usually, a mounted .dmg will have an icon of a plain white external drive on the desktop, like this:

If you're not seeing any drive icons on your desktop, that would be because they're off by default. From the desktop, choose Finder > Preferences from the menu bar. Under the General tab, turn on the check boxes for at least the first three types of drives. They should all now appear on your desktop.

The name of the "drive" will usually be similar to the name of the .dmg. So until you dismount the pseudo drive, the .dmg is "in use". Like any other drive in the Mac OS, you drag it to the Trash, which will change to an Eject icon. Once the drive has been put away, then you can delete the .dmg file. Highlighting the drive and pressing Command+E will also dismount the drive. The very long way around would be to restart the Mac since a pseudo drive can't remain mounted between startups.

From there, you can decide whether or not to reinstall the Adobe Reader, or use Preview. If you leave the .plist and other small files on the drive softwater mentioned, it makes no difference. They're useless without the parent app which would access them. So the only thing they'd be doing is taking up a very small amount of disk space.

still cannot restart the computer (or shut down) and get the message "Finder cant quit because some operations are still in progress"

Okay, first press Command+Tab. Don't let go of the Command key. All running apps you have control over will be presented in the middle of the screen. If there are any running besides the Finder, keep pressing tab until an app other than the Finder is highlighted and let go of both keys. Press Command+Q to close the app. Repeat until the only app running is the Finder.

Now try restarting. If you still can't, press Command+Option+Esc. This will bring up the Force Quit Applications box. Highlight the Finder and click the Relaunch button. This will force the Finder to drop any process it thinks it's trying to do and relaunch.

After that, you should be able to, and should restart your Mac.

That is extremely bizarre. You may have accidentally entered a keyboard command to open a file window and all of its subfolders. The Finder was stuck and couldn't do that until a restart. But then, once you restart, the command is gone and shouldn't have been acted on anyway.

Are they all just file windows? If so, press Command+Option+W. This will close all open windows instead of doing them one at a time.

What is your Mac doing at this point?

Forgot you're using Lion. All of those windows and other things opening after startup are so called "features". If you prefer your Mac act like a desktop computer instead of an iPad, do these two things.

1) Open the System Preferences and click on the General tab. Towards the bottom, uncheck the box for Restore windows when quitting and re-opening apps.

2) Choose Shut Down or Restart. Uncheck the box for Reopen windows when logging back in.

Do you know how to get that back?

No, not sure on that one. I'm still mostly working in Snow Leopard where your downloads get their own file window in Safari. In the attempt with Lion and Mountain Lion to make OS X mimic the iOS (iPad, iPhone) with downloads doing a cutesy animation to a corner of the app, Apple made yet another once straight forward and easy to use feature harder to use and less useful.