Yes they all can work together. The data in home assistant should be enough.

Regardind docker or not. There is more instructions in the documentation how to build it from source. You can also run it from the jar. I need to check if this documented right now.

Yes, I try to make as most sense out of the data as possible. It is kind of a velocity matching. There is a settings menu where you can specify the speeds. Actual detecting them is a little bit more complicated since traffic lights etc need to be accounted for. If reitti detects something wrong, you can edit it directly on the timeline and set another transportation mode.