A.  I see that Anakin grows up to be a bratty teenager, but from that to Darth Vader is quite a stretch, isn't it?

No. It's not the bratty attitude. You have to admit, though, that he certainly has changed since Episode I.

Anakin's conversion to the dark side is a gradual process. It's happening already. You can see that he prefers to address problems with force rather than with patience. Slaughtering an entire tribe of Sand People is not the Jedi way.

George Lucas has stated in interviews that Anakin's eventual downfall has to do with his inability to accept the world he lives in, and the fact that he believes he's better than everyone else. That is a characteristic we were heavily exposed to in AOTC. We also see a scene where Anakin jokes about making people see things his way in something much like a dictatorship. While that may be seen as a teenager's trait in some people, we can't be so sure about Anakin.

At the very least, we can see that Palpatine is doing his part to bait Skywalker. He encourages Anakin's attitude by telling him he will one day be the most powerful Jedi ever, a sentiment Anakin himself echoes later on in the movie.

B.  If Anakin has to choose between loving Padme and remaining a Jedi, does it mean he's chosen to leave the Jedi order?

No. The wedding at the end occurs without the knowledge of the Jedi council. It's clear that at the moment it's a secret. This is once again, part of Anakin's refusal to accept the rules laid out before by the entire world around him.

C.  Who ordered the clone army?

According to the prime minister of Kamino, Jedi Master Sifo-Dyas was their contact on behalf of the Republic. At first one might think Sifo-Dyas was an alias and Obi-Wan was bluffing about knowing who he was, but then Obi-Wan then said Sifo-Dyas was killed 10 years before. No information is given about the identity of this Jedi, but Obi-Wan does ask Yoda and Mace Windu about him.

According to Jango Fett, a man named Tyranus approached him. (That would be Darth Tyranus AKA Count Dooku.) This may be part of Palpatine's plot to misinform the Jedi. As far as anyone knows Tyranus/Dooku is the leader of the separatist movement, and Jango Fett was the man hired to kill Padme Amidala, making the whole thing look like a separatist assasination plot.

That Dooku is somehow behind the clone army seems contradictory at first, as he was building an army of droids which ended up battling the clones, but that is really an answer to the next question...

D.  Doesn't Chancellor Palpatine/Darth Sidious win no matter which side wins?

Correct! Palpatine's plan is to divide and conquer the Republic. Count Dooku is a Sith. He's Palpatine's apprentice. The Clone Troopers are far superior to the droid armies built by Dooku, but the droid army gave Palpatine, as chancellor, the excuse he needed to create an army (an army which had already been manufactured by that time.)

E.  Why don't we see Qui-Gon as a ghost?

This question is still not really answerable, except that we did hear his voice in AOTC. Right after Anakin was seen slaughtering the Sand People, we see Yoda and Mace Windu meditating, and they hear screams, and among those screams is Qui-Gon saying "Anakin!" twice.

Is it possible Qui-Gon is talking to Anakin and no one else knows it?