[R] PvT end game economy / Base trade

I am a 4 month lurker in here, and finally decided to post. I am top 20 diamond player (usually between rank 13-17) playing protoss. I dislike cheesing, and I suck at starcraft II.
Im not playing too much at the moment, mostly just 2-5 games a day, but I did get around 250 games played during the beta. For those who care, my APM is around 100 in the average game.
English is NOT my primary language, but I hope I am able to make myself understandable.

I find myself often losing a late game match vs a Terran when it gets around 25 mins long of a game. I don't know if it because I'm getting tired and losing focus, or if my end-game unit choice is poor, or if macro is too bad, or whatever.Therefore I decided to upload this replay of a game I just played, not because it is special in any way - on the contrary, it's like every PvT I play at the moment.

I feel that I am "containing" him decently, and he has trouble getting the third up, and since I am getting my third up, I could win the game like that. However, I chooses to ignore my army and goes straight for the base trade. When I looked at the replay, I was really in doubt if I made the right move. I mean, when do you EVER win a base trade vs a Terran? But going back to defend, he could already have destroyed half of my base, and dont think I would have been able to win the battle with a big enough advantage to go back to his base and take the game.

So I guess my questions are;
Should I have went back to base to defend, or was accepting his basetrade proposal the correct move?
Was i being too aggressive, and should have been getting my third up while being defensive, instead of trying to harass with colossi?
What do you notice as the biggest problems in my general play?
The last question can be anything, I just haven't uploaded a replay here before, so any advice you feel I need will be greatly appreciated.