Is the Queen's Gambit a good move?

In short answer, yes. It is a good move because a quick loss of a pawn will mean a closed checkmate quickly. So to answer your question: Yes

Yes, The Queen's Gambit is a good move. 

Nope. People just accept the gambit at lower level.

It gets so typical against human players, that I had 4 or 5 missed wins in one game, then got that same exact sort of position a short while later which I won in 10 moves. (That's on my profile, the rapid game with me playing white and winning in 10).

Gone back to 1.e4. Learn about that more first.

Assuming you are referring to 1. d4 d5 2. c4, yes. It is frequently played at the highest levels and leads to a variety of options for both sides. You can look into the statistics here
https://www.chess.com/openings/Queens-Gambit

Starting out most players tend to play 1. e4 rather than 1. d4 because the games tend to be more tactical, so this can help you to improve your tactics faster. But there are plenty of tactics that can arise after d4 as well -- and it can give you an advantage over other beginners who are only familiar with 1. e4 openings. 

I'd rather play 3. e4 in the accepted variation.

It's certainly objectively good, but I think it's better after having learnt more about the game.

If I play d4 again, it'll probably be one of the system openings.

Right, but this is refuted by 3... e5. That is why the mainline is 3. Nf3, to prevent e5, but no one at my level knows it, so then I just play e3.

So e3 and e4 aren’t the BEST moves.