How do puzzle solving improve your chess?

I am a chess player with a ambitious goal of reaching 3000 elo at blitz chess.

The only winning idea in this game came from understanding the pin. I thought that knight move can't be a good move. This is a skill I learned mostly by solving chess puzzles. It became like buzz word that he did this, it's good and he did that it's not a good move.

The most winning idea of this game was double attack. After he decided to take his pawn back. Other things were easy. I think the game was resignable after that blunder.

You should know that solving chess puzzles is very important. I am working on easy chess puzzles and trying make simple tactics simpler. That is the only difference between me and Magnus Carlson. I solve a puzzle in 5 seconds and he solves it in 0.1 second. That is why higher rated players never blunder because they saw these patterns hundreds of thousands of times. Opening chess matters zero. I beat them by e3 opening so you can see that these openings are meaningless in blitz chess.

I am creating These forums because I want people to know that nobody solves hard puzzles while playing blitz. If you play on rapid and classical chess, you should calculate. But in blitz not

If you want to do more puzzles, there are other websites that allow you to play as many as your heart desires. Keep doing them until you're able to recognize patterns pretty well.

For reference: lichess.org has free very high quality puzzles.

I reckon that the game is won or lost in well over 50% in the opening. Just be well versed in all the traps in the beginning (and there are a lot of them to beware of) and u should have a good game. Ps never rely on your queen

puzzles reinforce habits that weaker players havent fully developed, and for stronger players, provide the needed visualization boost that quickly degrades if one doesnt do any chess in the short to mid term. Also good puzzles enhance pattern recognition of relevant tabiyas. Often the difference between spotting and resource and never once considering it is exposure to the abstract idea in puzzles. 
take for example the smother mate with the knight, this is not that hard to find on its own but what if its the result of a 5 move variation in a branch of lines to consider? knowing the tabiya lets you truncate an entire line of calculation to that well known tactic.
In my case for example, they are plenty of tabiyas i now look for that i would be far less likely to "see" if i didnt do lots of chesstempo, for example, backward knight moves, diagonally cutting through with a king in rook vs passed pawn problems, getting crucial in between tempi with a pinned piece tactic etc etc.

You may hear many facts like it helps with pattern recognition. That is true, but when i was a beginner i found many new ideas thanks to puzzles. many tactics like the greek gift were new to me at the time. Also, i do think some puzzles do get useless after a while, like the back rank mate puzzles, but still there are other complicated versions of backrank mates, so im not complaining. But i wont recommend only doing puzzles, something that helped me in getting to 1500 from 500 is definetely learning thru engine as well as tutorials. The engine gives you very few variations, ur gonna hvae to find new variations elsewhere and then test it. I would recommend puzzles for endgames as well. Because a lot of the puzzles are very good for engame practice as there is a variety but also same concepts. 
TLDR; puzzles are good, but u can do more than just puzzles.

I like puzzles because there's a solution to them, whereas you don't always know if there's a solution to your position in a game. In a game, maybe your position is a puzzle for your opponent to solve. Maybe you're the one who's about to get picked apart with the right moves from your opponent...

My lichess.org account is farhad5269. You can see my puzzle storm history. I am doing 20 runs everyday and analyze my mistakes and take screenshots from them to analyze them into the future. I have to tell you those are very good. I love to solve chess puzzles. I am not saying I am so good. I have to get to 100 score and keep practicing until I become so good at puzzles

The main function during playing chess is pattern recognition.

Good puzzles give you exactly that, but in a concentrated dose.