Good first time effort.
Yes you are leaving pieces unprotected and missing that they can be taken.
Keep playing the game and through time and experience this bad
habit will disappear.
It won't take too many games and you will suffer a few bad losses.
This is part of the learning process.
Look at each pieces before you move, is anything attacking it?
Look at the square before you move the piece to it. Is it protected?
Here are a few tips.
One aspect you must become good at it is visulistaion.
You must, and this will develop through time and play,
be able to see what will happen on the board after a series of 'forced moves.'
These are good. You make a move and you know how your opponent
is going to reply so you can then plan ahead what to do next.
Hopefully this will be something nasty for your opponent.
You can force your opponent's pieces onto squares that make things good for you.
An opponent's piece may be guarding another piece or an important square.
If you can lure that piece away from it's guard duty with a forced move,
then you can take the unguarded piece or put a piece on an important square.
Removing the Guard from an Important Square.
Here is a postion from your posted game. Look at it.
If the White Queen was not on d2 then Black could play Qe2 checkmate
(The Knight on c3 would be pinned to the King so cannot move)
e2 has beome an important square.
So you now think like a chess player.
"How can I remove the White Queen from guarding e2."
1...Bxc3! forcing White to play 2.Qxc3 Qe7 checkmate
(in that position White would have to give up his Queen else be mated)
White too had his chance.
Chess has a habit of biting you back if you do not take your chances.
In this position from the same game. you are threatening checkmate
on e2 as in the above diagram.
It's White's move. White played 1.Bxg7+
A good move. It wins a Rook.
Here is a famous piece of advice that you must now remember forever.
If you see a good move, don't play it, sit on your hands and look for a better move.
OK over to you. Same position. Find the better move for White.