Let me guess, running Motorola's stock ROM? I'm so sorry for you. Funny, my mom uses her Droid all the time for gaming, emails, news, and doesn't even manage to have the problems you're having.
"Wrong apps launch when I press their buttons". What? Come on, I've never heard of that and have no idea how that would even be possible unless you're using LP/ADW.Launcher's custom shortcut functionality...
EDIT: I think I know what people are referring to, especially after reading one of the child comments here... when you are using an App, it can use an Intent to launch an Activity of another application to provide some piece of data. If you leave during that flow and come back to the original app... it can appear that you are still in the secondary app launched by the first.
It's not the "wrong" app, you just left the application in an awkward place and Android is trying to help you out.
FWIW, I've had the wrong apps launch on my phone as well. I'll click an icon and something else will come up. So, I'll just assume I fat fingered it and go back to the home screen, but when I press it again, the same thing comes back up. It generally stops doing it after a few tries, but it is pretty annoying.
EDIT (to respond to your edit): I've had instances where opening the browser app opens the text message app, which definitely isn't a normal intent for the browser to use.
I had something similar happen to me on my Incredible once or twice. I can't remember if I hit Twitter and it went to GMail or vice versa.
It's odd that Twitter was involved for both of us. I wonder if they're doing something weird ... though I don't know any android.permission.CONQUER_OTHER_APPS permission in the API.
"Wrong apps launch when I press their buttons". What? Come on, I've never heard of that and have no idea how that would even be possible unless you're using LP/ADW.Launcher's custom shortcut functionality...
EDIT: I think I know what people are referring to, especially after reading one of the child comments here... when you are using an App, it can use an Intent to launch an Activity of another application to provide some piece of data. If you leave during that flow and come back to the original app... it can appear that you are still in the secondary app launched by the first.
It's not the "wrong" app, you just left the application in an awkward place and Android is trying to help you out.