Does learning the Dutch Defense mean you also learn Bird's Opening?

Seems the same to me.

...depends on the ornothology in the Netherlands...a bird in the hand is better than two in Denmark.

The key difference to note is that in the bird your opponent has not commited their d pawn 2 spaces (it is already on d4 in the dutch). This means that black may more easily force through e5 (as opposed to whites e4) with the help of the d pawn on d6.

However, they do share similarities, especially if black plays ..d5

Colors reversed...If you learn the Sicillian, do you learn the English with the advantage of a tempo?

No.  

Definitely NOT!  Against 1.c4, I can play 1...e6 or 1...c6, preparing 2...d5, putting you into either a Reti or Queen's Gambit Declined/Slav.  That is White's choice, depending on whether you decide to play d4 or not play d4 and play something like Nf3 and g3 or b3.  Either way, you are lightyears away from Sicilian Territory.

Same thing goes for the Dutch versus the Bird.  As already mentioned, with the Dutch, White has committed to 1.d4, making it harder to gain control of e4.  Black hasn't done such a thing.  The extra move is not always a good thing.  Many of Black's Defenses are based on White doing something committal.  White can't try to do the same thing.  White, instead, should be trying to attack since he has that move advantage, not mimic some defense when those defenses are reactions to moves already committed.  Does Black want to play ...f5 against both e4 and d4?  No!  He played 1...f5 because White committed to 1.d4.  That's why the extra move in a Defense does not constitute an advantage.

Sincere thanks to Thriller Fan...obviously, you know a lot more about the game than some of us.  I could learn a lot from you.  Thank you again for taking the time to guide me to a deeper understanding of the game.

Since I started learning dutch defense, I also play bird's opening.  Most of the same ideas work except that you have to know the lines where 1 tempo makes a lot of difference.  Some line that works for bird does not work for dutch. 

If you play the stonewall system, it is the same because stonewall is slow and a missing tempo does not make much difference.  I don't play stonewall because it only works against players who don't know how to play against it. 

No. Reversed openings are very different. They look the same but moving first or second matters a lot. I have found that the white version of any opening that can be played the other way (eg. Reversed Grunfeld, King's Indian Attack, Reversed Sicilian, The Bird) is more reliable than it's counterpart except for the Tennison Gambit ( the reversed Budapest Gambit) which is unsound and busted. The Dutch is playable but has a shaky reputation. The Bird is actually quite sound and safe with many good continuations for white, but it's not played much at the top level except as a blitz or bullet novelty. The Bird should not be played like the Dutch; there's no reason to setup a Hedgehog and theirs no cramp to fight. Their are some weaknesses around e3 and the kingside overall, but exploit them are another story. If you're looking for a change from the usual, I say play it. You could do much worse. 

"GM Alex Yermolinsky likewise notes that GM Vladimir Malaniuk, a successful exponent of the Leningrad Dutch(1.d4 f5 2.g3 g6) at the highest levels,^[121][122] "once made a deep impression on me by casually dismissing someone's suggestion that he should try 1.f4 as White. He smiled and said, 'That extra move's gonna hurt me.'"

source:
https://en.wikipedia.org/wiki/First-move_advantage_in_chess

I vote yes.