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So, this happened to me in a game tonight, and I am not sure we played it right

Situation:

CSM Dreadnought assaults my Land speeder, and immobilizes it.

Next turn, I shoot the Dread with a land raider and immobilize it (the reasoning was, speeders can't be locked in assault, so the dread is fair game to be shot) (this is the first point I am not sure about)

After that, we have an immobilized dread and an immobilized speeder stuck next to each other, can the dread still assault the speeder?
(we played it that he could)

Yep, and the dread can attack the speeder during both player's turns (thought it shouldn't take too many auto pens to wreck it).

Krak is right. As long as the Dread is in base to base contact with the speeder then the Dread can assault it in the following assault phases, in fact IIRC, he can assault it in your assault phase as well as his.

You also played the shooting phase correctly as vehicles (the speeder at minimum, the walker with everything but non-vehicle units) cannot be locked in combat.

So you played it correctly

Yes, if you are in base contact with an enemy vehicle in their turn you can attack it.

Yes, page 63: "Units that still have models in base contact with a vehicle in its assault phase may attack it again, just as in a normal ongoing combat."