I got Bb4 as well.
I have used tactics trainer but I can't get my rating above the 1100s.
I have heard the term 'deflection'. Is it the same as 'remove the defender'?
But after all this and watching videos etc etc, I can't help but fell I'm not getting anywhere, because I just did it again: :X
Perhaps I'm expecting too much in such a short space of time?
I've also noticed that I can't seem to beat opponents rated higher than the 1000s unless they seriously blunder.
Have you tried Tactics Trainer ?
I've been watching aww-rats videos too (they're quite instructive) & Chess Mentor is fine but I wonder if those things are going to help you with your immediate problem. You really need to concentrate on playing good technical chess first - not throwing pieces away carelessly or leaving your king vulnerable to attack.
Every time you move a piece to an unprotected square, ask the question 'can it be taken on that square ?' & if I move my rook away from the defense of my king, can I be mated ? Think through the consequences of your actions & in time you'll do it automatically.
Also be wary of taking your opponent's discarded pieces because it may be a trap ! As in the first diagram of post #18 - taking the knight lost you the game.
On the subject of traps, I spotted a nice one in your second diagram above at move 20 where you played h3. I assume you saw how useful it would be to move your rook to h4 (threatening Qxh7#) if it wasn't for that black bishop guarding the square. How might you tempt that bishop off it's diagonal so you can play Rh4 ?
See if you can work it out for yourself but here's my solution:-
Have you heard the term 'deflection' ? At the very least you win material but don't worry, I wouldn't have seen all of this in a game of live chess when time is short.