Does Yoda know Dooku is Palpatines little buddy?

I'm confused about the whole relationship of Yoda, Mace, Jedi Council and Dooku and Palpatine. I only saw the movie once, but why is nobody extremely suspicious of Palpatine? I mean, Yoda, Obi Wan, and Anakin all fought Dooku...don't they realize he is Palpy's little sidekick? therefore, if Dooku is evil, wouldn't it just follow suit that Palpy is too? I don't get why the jedi don't just see this. I know there's the convenience of the 'clouding of the force', but puh-lease.

Also, when Yoda, Anakin, and Obi are fighting that battle...the one where they blast that big spherical ship and it falls back to earth (an amazing visual) who the heck are they fighting?

I'm just having trouble figuring out the difference between the Republic, the Empire, the Federation, the Rebellion, the Seperatists....

I only saw the movie once too, but it seems to me that these Jedi really arent all that bright. Common sense would dictate that they would figure all that out, but the Jedi are idios. Even in the beginning of the film, they say something like 'oh Count Dooku wouldnt kill anyone'

I think the jedi are about as smart as a box of rocks.

No, they don't realize that. The two never have the slightest connection to each other in public.

They don't even realize that Dooku is connected to Darth Sidious (whom they don't know to be Palpatine) until Dooku tells Obi-Wan.

That's a Trade Federation ship. The Trade Federation is a member of the Separatists.

The Republic is the big galactic government which is headed by the Chancellor and Senate, and which has the Jedi as a 'peacekeeping' force. Tatooine, by the way, is outside the Republic; it's in Hutt Space.

The Empire is what the Republic is in the process of becoming. It's essentially the same group of planets as the Republic, plus some new ones it will expand into. The Empire is different from the Republic primarily in its structure of government and its policies. But the Republic as of the end of AOTC seems to have become the Empire in all but name.

The (Trade) Federation is a small subgroup of planets within the Republic. They had a petty squabble in Episode I that Sidious/Palpatine took advantage of to advance the Sith agenda. In AOTC, the Federation has joined the Separatists.

The Separatists are a large group of planets which were formerly members of the Republic, and are now trying to get out. They're headed by Count Dooku. However, unbeknownst to most of the Separatists, Dooku is actually doing this in the service of Darth Sidious. Sidious/Palpatine wants to militarize the Republic and to suspend its democratic procedures, and the Separatists give him the excuse to do so. This is how the Republic is slowly becoming the Empire.

The Rebellion is a group which will (in Episodes IV-VI) oppose the Empire and seek to restore the ideals of the Republic. We don't yet know how it will be formed. Some people think it will grow out of the Separatists, but that would require a major shift in that group since they're already dupes of the Emperor-to-be. It seems likely that there will be involvment from a number of members of the Loyalist Committee, a group of senators who oppose the changes taking place in the Republic.

I think you forget that Yoda, Mace, and everyone else in the films are, unlike you, not SEEING the films. You have to put yourself inside a movie, especially one like this, to understand certain things. You have the original trilogy to look at, as well as what Lucas wants you, the viewer, to see. We get to see the sly look on Palpatine's face, we get to see Sidious and make that connection, THEY do not. Also, Yoda has given Palpatine a few 'glances' here and there, but, again, the Dark Side clouds things, and the characters in the film are not sitting on the outside and seeing everything. Keep that in mind. Also, there is absolutely no reason why they should think Dooku is Palpatine's 'buddy.' For all they know, they think it was Dooku who trained Maul.

That was a Trade Federation ship attempting to escape.

Because the Republic has already granted dictator-like emergency powers to Palpatine, whom we know becomes the Emperor.

... and the Jedi?