Assuming Twilight (though the principles are the same for DA, just that all races base speed is 1)
initial ship speed with no engines is 1 unless you are the Terrans/Drengin/Altarians where it is 2. The Arceans are a lil different: IIRC, they stll have an initial speed of 1, but it takes two passive techs to reach a speed of 2 (due to the -1 starting speed)
No.
Base speed in TA is 2.
Impulse is +1, Warp is +1, Hyperwarp (Drengin, Iconian, Korath, Korx, minor race, Terran, Thalan) is +1. Gravity Accelerators (Terran/Arcean/minor race, but trade good) is +1, Thalans get +1 as a neutral tech, and +1 as a normal tech. Arceans get +1/+2 from buildings (doesn't stack), but only if they're built on the planet in question. Terran tree gets +1 from innovation complex on one planet. Hyperion shipyard gives +1 on one planet. Terrans, Drengin, Altarians get +1 inherent, as Silver says.
Maximum guaranteed would be 4, whereas maximum would be 12 or possibly 13 (assuming Thalans go neutral, research the tech, and trade it). This would only be for one planet, with both the innovation complex and the hyperion shipyard on it, in addition to an advanced navigation center from the Arcean tree, and only for Terrans. If you pick up +2 speed at the start of the game you could actually hit 14/15 doing it this way.
@Silverbeacher
Stellar Folding does not give +1 speed.
Is there a way to check for bonuses that are specifically from trade goods?
No, but you can do it in a roundabout way by checking the diplomacy screen with all the races to see if someone has it available in their screen-if they do, it means you don't have the trade good in question. (No one can trade it but the owner and it won't show up if you have it built or have traded for it.)