You are both correct in your own way. The F-20 was an advanced variant of the F-5 which lost to the F-16. The F-5 was also a variant of the YF-17 which eventually became the F/A-18. The F-5 is still used for dissimilar air combat training and the T-38 is the trainer version, still in user with the AF for UPT.
The F-20 was never a competitor to the F-16 for US sales. It came later as an export alternative to the more expensive F-16.
No. There is no link other than Northrop. Not a variant, not an evolution.
Completely different aircraft.