Question: What kind of disease did Tommy (one of Johnny's friends) succumb to?
Answer: It's implied to be a combination of brain damage (Johnny suggests this to Miguel earlier) and cancer that spread to the brain. In real life the actor suffered kidney and liver failure and died not long after.
Question: Johnny punishes his Cobra Kai class after learning that certain members trashed Daniel's Dojo to try to get the culprits to confess (with no luck). Why didn't he just send them all to Daniel's Dojo to clean up the mess and fix it up? That would have been the more honourable thing to do.
Answer: He was trying to flesh out the actual culprits but, as you pointed out, he wasn't having any luck. But if he hadn't received the phone call, he might have sent the entire class over to clean up. However, in the same episode, check Robby and Demitri's reactions to the former Cobra Kai students joining Daniel's school. Tensions were high between the two dojos and Daniel's anger at Johnny's dojo might have convinced Johnny that the current students would not be welcome there (risking a fight which both Johnny and Daniel wanted to avoid), so he might have been reluctant to send anyone even if it was the honorable thing to do. Also, Johnny mentions in an earlier episode that there is a difference between mercy and honor. He wants to make sure the real culprits get punished properly. Once he discovered who did it, the innocent would be off the hook and then the real punishment would begin for the guilty. So, in closing, there could be any number of reasons why he didn't send the entire class to clean up Miyagi-Do.
Question: Silver tells Chozen he's never had any children himself. If that's the case, then how are people calling Snake from part 3 Silver's son?
Answer: I've seen the 1989 movie many times and never once did Silver ever present Snake as his "son." Snake and Dennis were two young men who simply worked for and/or lived with Silver and only called "the boys" when Mike first arrived.
I never said it was said in the movie. I said people are saying it. Social media. Etc.
Simple, people don't know anything and assume baseless things for absolutely no reason.
Answer: When the movie came out in '89, it was revealed that the director's son had a part written just for him as the villain's son, and he would be called Snake. This relationship, however, was never addressed in the film itself and Snake just became a member of the house staff for Silver.
Answer: It isn't said specifically, but Tommy does mention that "it's in here now" while pointing to his head. This suggests some sort of cancer has spread to his brain.
BaconIsMyBFF