The problem I'm having with this patch is that when I try to get in one of my guns in a bomber I get a message that I'm now in vehicle mode.
The message may be an error. You are actually in "Bomber" mode. If you do not want the game to auto-select the controller mode, then uncheck the "Auto select mode" option in Options->Controls->Map Controllers. If you do this while in the game, you will be in the last mode the game selected. You can either start another sortie, exit the arena, or manually select the mode, if you have mapped those commands to any buttons/keys.
I downloaded the game off the website and lost all of my settings and skins. Is there a way for me to get them back?
They are not lost if you did not uninstall the old version before installing the new version.
There was a change to the full game installer though. It will force the installation into a folder named "Aces High III". If your original game installation folder is not named that, then look for the "Aces High III" folder in the original game folder. That is where the game is running from.
If the above is true, then copy your old "settings", "skins", and "ah3terr" folder to the new installation path.