Can BTT do this?

For years I’ve used a separate macro keypad to the left of my keyboard so my left hand would be useful for one key to either close a window, close a program, archive an email, etc. I no longer want to use a separate keypad for that but would like to program key presses on the far left of the Mac keyboard to accomplish the same thing.

For example, I would like to double-tap the Control key to do what Command+W does. If not double-tapping, then a combination of keys on the far left side.

Is BetterTouchTool the best app to do that?

yes, you can use key sequences for that.