How are you training tactics? puzzle question

I'd say no. I don't think puzzle rush is giving you the exercises that are most beneficial for you during a game. The beginning puzzles are so often just mate in 1, 2, 3 and almost never a double attack or a pin. In low level games, the reverse is true. Those games get decided on spotting the double attacks and the pins. Those are more important to practice. I think other chess puzzle sites (and puzzle books) do a better job than chess.com's puzzle rush.
Another thing that you likely don't learn about and that doing puzzles won't improve, is to have a good method for finding tactics. It's this part that is often overlooked and, I believe, causes some players to have high puzzle ratings, but low other ratings. It's one thing to know there is a tactic, but another to have to find it when there might or might not be one.
Good puzzle solving strategies are based on the following elements: finding the right targets and finding the right moves. The following things can be targets of a tactic: a king (check), a checkmating threat, or pieces (pawns too in games of course). With pieces, you'd have to specifically look for the following. Are there pieces that are completely unguarded? Are there pieces that have a higher value that I can attack? (for example: attacking a queen with your knight). And: are there pieces that are insufficiently defended? In the last case, I don't mean literally insufficiently defended right now, because then you can just take the piece. I mean the situation that you don't win anything by capturing the piece right now, because you'd just be trading pieces, but if you would somehow be able to add an attacker, that would threaten to win material. A simple example: you're attacking my knight with your bishop, and my bishop is defending my knight. You can take my knight with your bishop, but I'll take your bishop back and it's only a trade of a knight versus a bishop. But if you'd be able to attack my knight again, with say your queen, now suddenly you not only take my knight with your bishop, but you also can capture my bishop when I take back your bishop, after which you end up a piece up, because you've taken both my knight and my bishop, while I could only take your bishop back.
Apart from the targets, you need to learn to look at the right kind of moves. Tactics almost always use forcing moves. This is a difference between just attacking a piece and hoping your opponent doesn't see it and a real tactic, where your opponent has no choice but to lose the piece. So if you're looking for tactics, you need to look for forcing moves. This is where the targets become important again. If you put your opponent in check, it's the most forcing move there is. He HAS to do something about check, it's in the rules. If you threaten checkmate, I better do something about it, because otherwise I'll lose next turn. Then again, if I can immediately checkmate you, I win, so it's not as forcing as a check. If you attack my queen with your knight, I should probably again do something about it. See, all of those moves force me to respond to your move.
If you look at your possible targets and then at the forcing moves that can be made against them, you will encounter 99% of the 2-move tactics, if they're there. Effort and experience will teach you which forcing moves probably won't work. That's important too, because it'll help you in a real game discarding some of the forcing moves that you might want to look at. Effort and experience will also teach you that, for example, checks should always be investigated.
Using puzzle strategies is essential to finding tactics reliably during a game. At first they'll cost a lot of time. That's why you would do well to practice it during the puzzle training. It's not just important to get the right answer, also how you get there is important. Of course, no grandmaster is sitting down at a board and actively using this puzzle strategy. That's because it becomes intuitive. When a strong player sees a puzzle, the first thing they automatically do is to check the checks. And that, combined with a lot of pattern recognition from doing so many puzzles, means they'll find tactics in fractions of a second. When you're starting out, it's not intuitive yet. By just doing puzzles, you'll work a little bit towards that intuition. But by actively trying to teach yourself good solving strategy, you'll make that process a lot faster.
Tactical awareness isn't something you can learn, you either have it or you don't. And if you don't then tough luck.
Tactical awareness is definitely something you can learn
No, it really isn't. Sure, you can learn stuff like what a fork is and to look for them, completely different applying tactics in an actual game.
Tactical awareness is definitely something you can learn
No, it really isn't. Sure, you can learn stuff like what a fork is and to look for them, completely different applying tactics in an actual game.
I literally typed out how to do it. You think that strong players are just born with it? Immediately know how to not blunder pieces away when they play their first game? Come on.
Tactical awareness is definitely something you can learn
No, it really isn't. Sure, you can learn stuff like what a fork is and to look for them, completely different applying tactics in an actual game.
I literally typed out how to do it. You think that strong players are just born with it? Immediately know how to not blunder pieces away when they play their first game? Come on.
Not immediately, but within the first few months of learning the game because they have that natural talent. You can put in all the hard work studying and training all you want, unless you have that natural talent you won't be accomplishing anything.

pb 3600, rush pbs 30/40/72:
rush builds intuition & pattern-recognition;
survival develops analysis & calculation skills.
take your time trying to get every puzzle right, review missed ones for the proper solution & try to verbalize a lesson from each mistake.
('check the material count first', for example.)
remember, though you can back out of an untimed puzzle & tackle it later if you need to:
don't 'quit' survival or you'll lose your progress.

After playing more games, things just started appearing to me. Maybe it was lessons, puzzles, analysis, seeing tactics that were played against me, tips and tricks in YouTube videos, etc.

Hi , I saw the diagram without using board and find out that the best way is Q-d8+, well, now if block capture the Queen by knight , white will win with e8++, and if QxQ then c7xQ+ and no way but Nxq ....and now is the time of another checkmate by e8# again...thanks a lot .kapa

Doing chess.com puzzles is a good start, but you also need to apply what you have learned in your games. Play some games with 15 minutes or more and take your time to find opportunities to pull off these tactics. It's quite difficult at first, but the more you work on it the more experience you'll have from it. And with enough experience, you'll reach a point where finding them becomes natural to you. That you could easily find winning combinations out of instinct. Hope this helps :)