Changed my gamer tag and now I can't sign into my profile on any 360 games

If your email address and password haven't changed it should be the same. Did you use an email address that already had an account attached to it? Try logging into it on Xbox.com. In regards to the games I'm not 100% sure how it works if you used one of
the new system names. Like "Geo#49410", if not you may have to just redownload the account with the sign in feature if it was corrupted for whatever reason. Your game saves should also update to the new username. Hopefully this helps somewhat

I just removed my profile from my XBOX one account and then added it back in with no problem. When I go to play a 360 game and try to download my profile, it keeps telling me that the password is not correct. Please advise.

Delete the profile in your storage settings and redownload it completely with your standard email and password.

So i see one issue... my gamertag was changed from to CLOWNninja yesterday but didn't seem to go all the way through as your replay indicated? Please advise.

Your xbox account is associated to your email, so changing your gamertag doesn't affect, in case you can't remember your password you can recover your account following the steps on this article:

https://support.microsoft.com/en-us/help/17875/microsoft-account-reset-or-recover-password