I do love that story. Although I think you are trying to test or confuse this old cat. F-2, F-4 ? Then I figured out you probably meant the F-102:
And maybe the F-104:
Although since the F-104 did not have an internal weapons bay (It was armed with the M-61 Vulcan Gatling cannon, and sidewinder missiles) You might have meant the F-106 which was really just a developed F-102, but it was indeed faster. The F-104 was a lot faster, but short legged.
Of course your second story reminds me of a story as well. This one from a guy who was a Major when I first met him. (He had other stories, but they weren't suitable for this forum :) ) He was a navigator on a prop driven cargo aircraft. Flying it from Da Nang to CCK (on Taiwan, where they had some maintenance work done).
They had been instructed to fly as close as they felt comfortable to Hainin Island, which is and was Red Chinese. (It's where the P-3 landed after the Chinese jet ran into it).
Well a Chinese MIG clone came up and formed on them. They were looking at him, he was looking at them. The navigator flipped the MIG pilot the bird, the old one fingered salute. The MIG then pealed off, flew behind the transport and made a high speed pass from aft to forward, then turned around and made another from front to back. Then the MIG formed up on them again. The pilot looked over at them, and gave them the "Roman salute" (slap left hand on right bicep, with right elbow at a right angle, upper arm horizontal and in front of the body palm inwards with fist clenched. IOW "Up Yours!".