Question: This movie shows Jason Voorhees didn't drown in Crystal Lake in the first movie because he's shown to be alive in this movie. It's a known fact that the kid Jason Voorhees can't swim, so how exactly did he avoid drowning in Crystal Lake?
Answer: That is indeed a plot hole, and up to speculation. The best guess is that Jason somehow made his way ashore, and chose to hide in the woods rather than face further bullying from the rest of the kids.
Question: What happened to Paul? If he was killed, why not Ginny as well?
Answer: In the original draft of the script, it was heavily implied that Paul was killed by Jason and Ginny was the only survivor. And in fact, an alternate ending was filmed showing he died. However, any direct references to him having died were removed from the final film during editing (in part because the special effects were deemed "too silly"), and his fate was instead left ambiguous. There is also some SLIGHT evidence he may have survived, as a radio broadcast in "Friday the 13th Part III" says eight bodies were found at the camp, only only eight people at the camp died on-screen. (Paul would have made nine). But ultimately, it's left up to the viewer to decide whether you believe he's alive or dead.
Answer: It's evident that more must have happened after the fade to white as we last see Jason grabbing Ginny, and then later she is found by authorities while Paul is not. One likely possibility is that Paul had intervened and succeeded in freeing Ginny from Jason, but in doing so became a victim himself.
Question: How was Jason able to find out where Alice Hardy (the girl who killed his mother) lives?
Answer: It's possible that there was a media blitz of her being the sole survivor of the massacre, including where she was residing. Jason may have been a psycho, but he might have enough intelligence to figure it out.
Question: This question applies to this movie and all the other movies where Jason is the killer. Whenever Jason is unmasked, why does his face always look different from the previous film?
Answer: Quite simply, different crews and effects teams worked on different movies, and they wanted to put their own stamp on the character and do their own interpretations. They also understandably wanted to make him look more and more monstrous and scary with each film to try to "outdo" the last one.
Answer: This particular film does not address this, and seems to imply that Jason didn't drown and grew up living in the woods as a psychopath. Later sequels heavily imply (or outright state) that Jason was brought back as an un-dead creature by unknown supernatural means and cannot be killed in a conventional sense. As it stands it is best to view Jason in this film as un-dead, as the number of films that show him as supernatural far outweigh those that show him as a normal man. The character is generally remembered in popular culture as un-dead.
BaconIsMyBFF
I think that the whole franchise didn't take much care of continuity (for example, in part 2 Jason is a woods-boy full of beard and hair, in the third he is taller and bald), but it's explainable to the fact that Jason managed to survive somehow, never told his mother he was alive (even because the camp was closed many times and Pamela never showed up frequently), watched her die and took her place for revenge. We always have the feeling that there's something supernatural in Jason, since he never dies he can be hit with axe, machete, fire and even hanged up, and he is still alive, but he definitely becomes something supernatural only from part 6 further. Yes, seeing as the story starts, it could be simpler to think Jason somehow returned as a ghost, as an Un-dead man, but in the first half of the franchise they gave a bit of reality to the thing.
What information in this sequel gives any indication that the kid Jason didn't drown in Crystal Lake?
Athletic Jason
The fact that he's a full-grown man instead of a young boy. The fan consensus, and the original intent of the filmmakers, is that Jason is a human being, albeit extremely tough and completely insane, in parts 2-4, and comes back as an undead being in part 6.
Jukka Nurmi
That's valid along with the small house in the woods, except that doesn't explain how a kid that can't swim didn't drown in Crystal Lake.
Athletic Jason
Luck, misinformation, etc. Yes it's vague, but a lack of explanation doesn't entirely constitute a mistake.