F-14... was there any competition? Features from the F-15 alternate
designs showed up on the Tomcat.
There was, the F-14 was selected when the F-111B failed to meet
expectations.
Whether they were in direct competition at any point I don't know, but on
paper they must have been.

F-15... McDonnell-Douglas, Rockwell, and others submittted competitive
designs
F-16... YF-17 Cobra (which influenced the F/A-18 Hornet)
And later lost out to the F/A-18 in the Navy competition (a navalised F-16
was proposed but rejected despite being pushed heavily by the white house)

F-20 Tigershark... private venture, no one wanted to buy it
Piper Enforcer and ARES Mudfighter... no interest in COIN aircraft
Never competed against the F-16 or each other. ARES was a technology
concept, Enforcer was aimed at the 3rd world market, in part for use in US
military aid projects. Those were pretty much stopped before it could enter
production

Both the Tigershark and Enforcer were meant as replacements for the F-5A
series, potential customers bought the USAF choice instead...

A-10... Northrop A-9
F-117... Northrop XST (and unknown to the USAF... Germany... the MBB
Lampyridae)

Lampyridae was never in competition to the F-117. It was a separate
development of which only a few photos of a single model exist.