The Sparrow had its own challenges from what I've read. Specifically issues with the acquisition radar being able to track a fast moving target and the missiles ability to receive the reflected signal and apply the right amount of correction. Got to remember that the time when these missiles were being developed it was to target slow moving bombers - not tight turning bandits.
https://www.amazon.com/Sidewinder-Creative-Missile-Developme...
The rest ... were a liability for years.
US pilots also had the bizarre order to visually identify targets before shooting (which then meant waiting 4 seconds for the missile to arm before actually firing it.)
Amongst other things, visibility in the tropics is often not 4 seconds worth, and the enemy can use clouds to get real close.
0. https://combatace.com/forums/topic/91818-the-f-4-phantom-and...
And yes, had nothing to do with guns. Guns are and have been obsolete on fighter aircraft for decades.
The Vietnamese pilots were using Soviet tactics, mainly Ground Control vectors.
Most Vietnamese pilots were rookies, but they did have some aces who would dogfight, like Colonel Toon, who was shot down by Randy Cunningham:
https://en.wikipedia.org/wiki/Duke_Cunningham
But largely the tactics were to surprise the Americans with first MiG-17's, then have a MiG-21 at high speed do an ambush pass from the clouds through lower-flying Americans.
The Vietnamese could have done a lot more damage had they known how worthless the US air-air missiles were at the time. There were all kinds of problems with taking too long to arm (around 4 seconds) and vibration from takeoffs and landings inerting the missiles. And that no gun thing.
Additionally, US pilots were expected to have up to a dozen radio channels active, causing pilot workload problems until they turned off like 11 of them.