My assessment of dogfighting capabilities would be my own personal assessment. That would not be worth sharing, because it's not backed up by testing. The government is conducting operational testing now, but all you'll see made public is encapsulated here:
http://breakingdefense.com/2015/07/dunford-mulls-f-35b-ioc-d...More developmental testing will occur over the coming years. But I have nothing public to share with you.
To answer your questions:
1) What do you mean by "visually track"? If you mean "with the good old Mark 1 Eyeball", no. The F-35 doesn't have the cockpit visibility of an F-16 or something like an Su-27/35. Now, if you mean, with avionics, then yes, far better. Check out this video on the EODAS: https://www.youtube.com/watch?v=9fm5vfGW5RY Spotting things hundreds of miles away is very realizable with this system.
2) Can the craft turn as well as an F-16?
Well, what kind of F-16? A clean F-16? That's going to be hard to beat even by a lot of combat UAVs. An F-16 with a usable combat load of bombs and A2A missiles? Yes, the F-35 has comparable maneuverability to this configuration of F-16, AND it carries all that ordnance and fuel internally, maintaining stealth. Check out the maneuverability section of this excellent resource for more info: https://comprehensiveinformation.wordpress.com/
3) Does the cannon fire reliably and with enough ammunition to do its jobs?
In ground tests, yes, it does well. The first in aircraft test was done last month (https://www.youtube.com/watch?v=R1HJjcVIuJg). It fired 10 rounds without problems. More testing to come in the future.
Basically, he has an idea of the plane in his head -- like you seem to have -- and he's bending all the facts to this narrative. It's a thing that humans do. But all this reads very differently to someone who looks at this stuff every day.