What should I learn at 360 to get to 500 ?

I went up to 400 in a single day out of sheer luck, then fell back down to 280 range, I have been doing a lot of tutorials and puzzles since. I am still unable to develop a strategy to handle my opponents. I still feel lost a lot.

Although, The tutorials have made me stronger and calmer I am back to 360. Question is what should I learn in order to improve further. The tutorials helped me go on a 9 game winning streak. That felt nice.

Also, how long does it take to become fluent in notation, (i.e. d4,e6,c9...blah),  ?

Keep up the good work and the more you do the better you'll become. The key is passion for chess and that what you're doing fills you with joy.

While it is easier said than done, the answer is don't hang pieces. 

Gotham chess recommends Indian defense and london system for attacking for beginners

You should play 30 minute games and think through each move thoroughly to make sure you don't blunder.

Here you go:

https://www.chess.com/blog/nklristic/the-beginners-tale-first-steps-to-chess-improvement

If you put in the time and effort, you can go much further than 500. Opening principles and not blundering pieces will get you over 1 000 for sure.

At 360, your games are dominated by who makes the worst single-move blunders that the other player sees.  Strategy comes later; the first thing is to stop throwing away pieces.  Your strategy right now should be "don't lose stuff" and "capture their stuff, safely."

Here's an example from this game, on move 18:  You move your knight to d3, where a bishop captures, you capture back with your bishop, then they capture with a pawn and you've lost a knight and a bishop in exchange for a bishop.  A little later, on move 21, you threaten their knight and then they move their rook and just let you take their knight for free.  Each of you made single-move blunders of pieces like four times in this game.

(Also, there's the blunder that didn't happen, on move 9, where for three or four moves, if white moved f5, you have no way to save your bishop, but neither of you saw it or did anything about it.  Edit: This makes the engine go nuts because each time you fail to take the pawn on f4 it says you blundered, then each time your opponent fails to move it to f5, they blundered.  Finally you ended up taking the pawn.)

1) Try playing slower games.  30 minute games will give you a lot more time to consider whether you are making a move that loses you a piece.  With every move, you should first be asking "Will I lose this piece and get nothing back?"

2) Always look for, in this order, checks, captures, and threats when you're looking for prospective moves, on the ENTIRE board.  Don't just play them.  Ask yourself whether they leave you better off than you were.

3) When you have a move you like, look at what your opponent will see after you move, including checks, captures, and threats.  Those are the moves they'll use to force you to do things you don't want to do, or punish a mistake.

4) Remember that having tunnel vision about the move they just made might distract you from a more important thing happening elsewhere.

5) Remember that bishops, rooks, and queens can have critical effects from all the way across the board.  You need to know where they are and see what they threaten.

It takes a lot of time and practice to improve this.  I'm currently around 900 rapid and my games are still dominated by these problems, but as my score increases, it's to an incrementally lesser degree.

As far as feeling lost:  If you really don't see a meaningful move, try seeing if you can protect a piece with a move or maybe head off something you think your opponent might do by threatening an empty square.  Or, think about whether you can develop a piece still in its starting location.

Regarding notation: It comes with time, meanwhile don't worry if you have to look at a board to figure it out.  As you read and use notation more, you'll start to remember common moves and where the squares are.  (But, you might always practice with the "Vision" trainer under the "Learn" tab on the chess.com website!  That's specifically for practicing notation.)

Do puzzles. Easy. 

Good advice, I will try to use also. The main thing I miss is a person threatens or captures and I can take the piece and miss it, especially when I have a pawn that could have captured the piece. especially later in games. Maybe I am nervous.

This is one way just do everything in your power no to give free pieces and take free pieces once you master that you will jump rating very quickly.

@Paleobotanical Thank you for the detailed advice. I will work on it.

Also I'd say  maybe play the Scotch game. It's a simple, attacking opening that destroys a knight and a pawn. Also highly recommend the Accelerated London System

@Paleobotanical, your advice was excellent! I thought you must be a 2000+ rated player to have such knowledge lol.

Hahahahaha no, I'm just living evidence that understanding the nature of my own problem doesn't mean I've solved it.

Thanks for the kind words!

A whole bunch of things.

You might benefit from Aman Hambleton's Building Habits series or at least the first parts of it. He has made himself a very simple set of rules that he follows and shows how you can play with them successfully at beginner level (he made a new account starting from 400 rating and going up from there). He basically just develops, castles early, moves pieces towards the center, captures anything of equal or greater value, doesn't leave his pieces hanging and uses the king actively in the endgame. In addition, the videos are extremely fun (he does tell, what he is not supposed to see and how can you easily improve). At further stages more complex rules are added and following them obviously needs more studying, but the first ones are extremely easy.

The first two ones get up to 700 rating and are here:
https://www.youtube.com/watch?v=axRvksIZpGc (rating below 500)

https://www.youtube.com/watch?v=WPmbUXQloHs (rating 500-700)

Start reading Silman's Endgame Manual and Irving Chernev's Logical Chess: Move by Move. You'll begin to understand the game and I guarantee by the time you finish both books you'll be well over 1000. At least.

You want to be high rated, how do you get high rated? You get high rated by having a chess brain that is high rated. How do you get a high rated chess brain? You want chess to be in your long term memory.

So how does something get to your longterm memory? By first having it in your short term memory. But not everything goes from your short term memory to your long term memory, only a small percentage. 

For example, if you study for a test on the day before you take a test, you remember more than if you did the same amount of study a month before the test. This is because not all the information did go from the short term memory, to the long term memory. 

So how do you retain the information in your brain, so that it resides in your longterm memory? By keeping your short term memory engaged with the activity.

Another thing that is important is percentage of the day you play. For example if you do 15 minutes of chess on a day, that means you get 1 percent chess information that day, which is a small percent of the possible 100 percent of information you can get on a day. 

It is also about the quality of information you want to have in your brain, for example if you only played versus players who are 100, you will retain only the information about the 100 rated players. So play against high rated players. How can you play against higher rated players? Play allot, the more you play, the more chance you have to get a winning streak, which makes you able play against higher rated players, the information you get from the higher rated players is of the best quality.  

The most important thing: don't stop playing chess for more than 3 days. Because having big breaks will not only cause you to lose all of your short term memory of chess, after a part of the short term memory entered your long term memory, the long term memory of chess will start decreasing slowly too. This will also decrease your true rating, which has to be regained again. Only after you have regained your rating, you can play against high rated players again, who will give you important quality information.

Everything that I would have said has already been said, but just remember to not get discouraged by your losses. Embrace them, and learn from your losses. 

When you learn from the mistakes you made, you will less likely make those same mistakes. 

Just follow what everyone else has said, and you should be 1000~ in 3-6 months. 

Also for the people who say: Don't blunder pieces. This obviously easier said than done, but if you focus on it, you will slowly start to see improvement, and you blunder less and less.