When you download the most recent copy of GameRanger from
here, it gives a step-by-step tutorial of how to install and run it. You can skip step 4, though (at least, for now). I'd write up another step-by-step but there's pretty much covers everything except adding RA2 to the list. I'm not in a very good position to explain that ATM so I'll let somebody else explain that when you get to it.
As far as Flash goes, have you tried updating it?
1. Go into Control Panel.
2. Enter Flash Player into the search box and click the top result.
3. Click the Advanced tab.
4. Click the Check Now button (before this, you may want to consider clicking the Change Update Settings button and enable "Allow Adobe to install updates (recommended)").
5. This should lead you to a webpage about the current version of Flash and give you the option of updating (if applicable). Mine is up-to-date so I'm not sure exactly how it would handle an out-of-date computer.