Need Some Help in Understanding This, Please!

For starters, I realize that chess engines and game analyses may or may not be helpful and probably shouldn't be taken as an absolute authority on what the best move might be. Still, for an inexperienced player, the engine and game review suggestions are the closest thing I have to a chess coach. 

Here is a board from a game I just completed against Engine Level 4 (Beginner). 

I am playing white and on the 9th move, I castled. The analysis called this a "mistake" and suggested a better move would have been Qf3, threatening to win material. I saw that move but I wasn't in the mood for losing my queen so I didn't really see the point in threatening the d5 pawn. 

Black then moved a pawn to f6, kicking my knight. I considered taking black's c6 knight, but figured I would end up losing either the bishop or my knight, wouldn't I? At this point, I'm not sure what I was thinking, but I did then go ahead and move my queen to fe.  And now the Game Analysis tells me I've committed a blunder! 

Why was Qf3 a "good move" on my 9th turn and a "blunder" on the 10th?  As it was, I made it through the game without losing my queen (an accomplishment for me) and I won by checkmate. 

But going through the analysis really confused me. Can anyone offer any insights? I don't see where castling was a mistake, so I'd appreciate any "human" analysis.  

Thanks so much! 

On your 10th turn, you now had several pieces attacking the knight: a queen, a knight, and a pawn. However, you only had two pieces which were protecting the knight: a pawn and a bishop. Moving Qf3 does not help the piece, which was in danger, and was, therefore, a blunder. This means that, after all the trades are done, black has gained material and you have lost some. For instance: 1.  fxe5, dxe5 2. Nxe5 3. Bxe5, Qxe5.  That's my guess.

Maybe it would have been better, after they moved f6, to capture the black knight or to retreat. I'm not sure. Is this helpful? I'm honestly not the greatest chess player, this is just my guess. 

What confuses me here is that black's position really didn't change with the pawn f6 move. It a move would be "good" at move 9 and the board is essentially the same for the next move... well, how could a previously good move now be considered a "blunder"? 

Obviously the answer is over my head at this point. On the plus side, I did go on to win the game, so I'm pleased about that. 

You could look at it this way:

try to stop thinking about the good moves and the blunders, and instead think about what black was trying to do. By playing f6, black is now attacking your knight three times. Your knight is only defended twice. 
Now you play Qf3, which moves your queen off of it starting square (which is always good) and attacks a black pawn. 
Black play fxe5 and takes your knight. That wins 3 points for black. 
You play dxe5 in order to protect you bishop. This wins you 1 point, so the score is 2 for black and 0 for you. 
Black plays Nxe5. This presses his material advantage and wins him another point. So the score is again 3 points for black. 

Ok, so now your queen is on f6 and blacks knight is on e5, thus attacking your queen. In order to defend the queen, you play Bxe5. This wins you 3 points and protects your queen from being captured. Now the score is 0 for both players. 

Black has one more advantage left now: Qxe5. This means that black can take the bishop, winning 3 points while not endangering their queen. And now they are threatening an attack on another piece: the pawn in c2. 

Castling may not have been a mistake, but a lost opportunity. If you had moved your queen to f3, depending on what black did, you might have threatened Nf7, forking the queen and rook and attacking the queen with the bishop. The queen would have to move and you take the rook. 

If after Qf3, black played ...Qf6 (preventing Nf7), you could play Nxd5, threatening Nc7, which would fork the king, queen, and rook.

When you played Qf3, it was a blunder because ...fxe5 and you've lost the knight.

What changed was that the ...f6 move "kicked" your knight. Ignoring such an attack is what made 10.Qf3 a blunder.

Bf4 is hanging; 9.Qf3 supports Bf4 & attacks d5 threatening 10.NxN winning material while threatening BxQ and discovered check when Nc5 moves.  You can harass the Q while picking off a few pieces. 9.O-O loses tempo.  10.Qf3 loses N & P and weakens center.  Position is quite different after 9...f6.

Black attacked your knight with 9. - f6. If you just ignore it and play 10. Qf3, you lose your knight for nothing. That is really really really bad. In this position, nothing else is as important as that. Nothing is even close.

I appreciate all the insight into these moves. It's complicated for me, and I haven't developed the ability to look too far ahead when it comes to exchanging material.  I will go over the game again and make a few notes! 

No, no, no. It is extremely simple. You only have to look ahead 1 full move.

They attacked your knight. They will take it, unless you do something about it.

You're right. I'm probably making this too complicated and overlooking the obvious. I'll try to be more watchful in my games today. Thanks! 

The answer is tactics! You are simply not seeing White's many tactical opportunities. With experience, you will!

Thanks for the encouragement! 

For the purposes of a gaining a better understanding of middlegame tactics, you might want to consider the book...

"The Six Power Moves of Chess" by William G. Karneges, which I review in my blog article...

Good Chess Books for Beginners and Beyond...

https://www.chess.com/blog/RussBell/good-chess-books-for-beginners-and-beyond

The review is in the Comments section following the main body of the article.   Or you can just search 'karneges'.

That position is actually a very good position for white, no checkmate pattern but still plenty of play.... The engine is funny because there is several potential best moves and the criteria is "will you dominate the position" and "is your position better than your opponent?" (Which is no the position is equal one pawn down both sides but black queen is in play and white queen on starting square but light square black bishop and king side black knight undeveloped) . So castles was a blunder? Engine expected you to make an attack and win some material specifically a queen trade? Yep, sometimes engine is like that, so you could take the knight on c6 with your knight and sacrifice the bishop if queen takes or if black takes back the knight with pawn then will lose the queen to your bishop which I doubt will happen... Best move to me is take the bishop with queen leaving c6 knight to reveal a check from bishop... Probably a few other things, I'm not sure of the level of your opponent and I'm not sure if you practice visualization to the point of a virtual chessboard and this is all I can memorize and type without proof checking what I wrote so if this is confusing it's probably my fault 😫 sorry