I think this plane actually began life as the F-5 Freedom Fighter. Also a trainer.
It has just kept on evolving.
No.
Completely different design than the Northrop F-5.
The F-18 began as the YF-17 that competed against the YF-16 for the USAF lightweight fighter competition. It was a completely new design, but lost to the YF-16, which became the F-16.
The YF-17 was brought back as the F/A-18 for the Navy, Marines and export customers.
Northrop P-530 then YF-17.
Neg, it started as the YF-17
The program was resurrected by McDonnell Douglas and presented to the US Navy as a replacement for fleet fighters and attack airplanes. That us how it got the designator F/A-18. Boeing acquired McDonnell Douglas and is now the manufacturer by title, but not concept or design.
The F-5 evolved from the T-38. The F-20 Tigershark was the next generation. The F-16 was chosen by the USAF instead. Only 3 were ever produced.
Iran actually developed and currently flies a newer version.