Is the Queens Gambit a gambit?

yes

No. Just no.

It's obviously a gambit, as black can simply take the pawn, which is not protected. 

It's obviously a gift, as you can simply take the gift, which is not protected. It doesn't matter that I will return this gift after a couple of hours and before that, I'll tell everyone how cool I was because I am courageous enough to play such a dangerous gambit! 

maybe and possibly

still a gambit lol

It entirely depends on White's 3rd move as with 3 e3 he is sure to regain the pawn but after 3 e4 if Black wants he can hold onto the pawn but reach a terrible position

Nah, white can not only win the pawn but get alot of dangerous counterplay if the Queens Gambit is accepted but it's dumb as nobody will accept the gambit and you're either playing against a QGD , a Slav or a Semi-Slav !

Well, the accepted is currently extremely trendy at Super GM level.

I guess because nobody told them about your groundbreaking findings.

I guess so!

It's a gambit.

Yes, white can win back the pawn, but he must make some concessions to do so.

If e3, then white has hampered the natural development of his queen bishop.

If e4, then white's d4 pawn is now weakened, as it no longer has a c-pawn to support it. (This is why one of black's most principled responses is an immediate e7-e5 thrust, to attack the now-weakened d4 pawn.)

So yes, it's a gambit. White offers his c-pawn, in exchange for other compensation.

And yes, he can win the pawn back, but he must give black some concessions in order to reclaim it.

Well , everybody's definetely heard of this :

This is already one of the most famous traps in the Queens Gambit even taught in theory by thousands of IM's and maybe even GM's and that's for Queens Gambit Accepted!

No one falls for this trap. It is probably the first thing you learn if you pick the queen gambit as an opening. The moves are intuitive (imho).

It is then why would it be called queens gambit

If White plays e3, he doesn't lose anything and still has their advantage. If someone will try to take back the pawn in 'real' gambits, they will lose the advantage. 

The right reaction to 4.a4 is of course 4...b4 which returns the pawn and takes away the c3 square from white's knight. 

3...b5 isn't the most common move, but it is entirely playable.

I have not seen those traps. 

Those traps are a kind of marketing stuffs by books, coaches etc.

1. You can play better by learning Classical lines .

2. If you are better, your will see better opponents and those cheap traps are useless against good opponents.

I wouldn't exactly say white has an "advantage" if he plays e3.

I'd say it's quite equal. Almost to the point of it being already drawn.

(Unless you're much stronger than your opponent, in which case, there's a good chance that you'll grind a win from the relatively even position).

I think that it's just a matter of definitions. Personally, I find the current name rather unfair to the Black pieces because if White will boast about their victory, they will point out that they played a ' Gambit ' !
In my opinion, the word 'gambit' stands for something dangerous, and it is always related to risk. When you play the QG, you don't face any dangers if you're White and you can always win back the pawn while Black cannot hold it. 
When people hear the word 'gambit', they believe that you're a courageous and cool player who's not afraid to sacrifice his pawn. It seems to be a little bit unfair.