Hello I was having the same problems and here's how to fix all of them. For that first error go to the civ4bts.exe (likely in your steam directory, dont use the shortcut on your desktop), right click, properties, compatibility, run program in win 7 compatibility, and change privilege to always run as administrator. Now start bts using the .exe (I run as administrator again just in case), you'll have to load the mod from the vanilla bts menu which will open up no problem. This means you cant use the launcher the mod comes with. However you can use the launcher to manage your modules and the changes will stick regardless of how you open AoE.
For the save issue you should first make a save file of a game at like turn 1 just when the game started. Next get in the habit of loading saves from the vanilla bts menu. It'll prompt you to restart as AoE which is what you want to do anyway. When you encounter saves not loading or crashing you open up bts.exe and load the turn 1 dummy save. It will load up no problem. From there load the big end game save you're trying to play.
Using these methods, avoiding alt+tabing, and restarting during prolonged gaming seems to help a lot with these bugs and the memory allocation issues.