recording keystrokes – left shift vs right shift

I want to send shift-F1 to an app from the touchbar, but does BTT distinguish which shift key is being held down while recording the keystroke, and send it accordingly?

In general yes, if you used the right-shift key it will show a little r:

However there are almost no other apps that differentiate between left/right modifier keys

that's true, but I'm glad that you implemented it because I'm using one of those few apps that does distinguish!

what does send key down and key up do? how can we utilize it?

sometimes you might need to keep a shortcut pressed for a while, then your first send the down events and later the up events