Is it safe to change between drive modes (Eco, Sport, Normal) while the vehicle is moving?

Also, can you go between regular and manual mode while driving?

 

Yes, going between modes is only changing ECU settings.

And yes, the transmission will adjust accordingly.

 

In addition to Swacer's response, you can also use the paddle shifters on your F Sport at any time and in any mode (D or M). It's also fail-proof so that if you try to downshift at too high of a speed, it will beep and prevent you from doing so. Similarly, if you are in M mode and don't manually upshift under acceleration, at redline, the transmission will do it for you.