I need to get informed
You don’t need to. There is no development plan, so §34 Building Code applies, meaning basically integration into the neighborhood, which will most likely be waived here because of the extremely atypical plot, at least as far as the extent of the structural use is concerned.
2 meters each on the other two sides.
Who says that? It is public traffic area and therefore the clearance distances may extend up to their centerline. So theoretically, building on the border would be possible, after all, the neighbor has done so too. Only with the parking space you have to maintain distance.
For the floor plan specialists here, you should draw the plot to scale, mark the exact location of the tree including its crown, safety zone (negotiate firmly again with the environmental office whether it really has to be 1.50m) and the boundary distance.