OP: We can define location, size, velocity for rupa. Can we define these for Nama ?
Location, size, velocity, shape, time, ... all these are conventional. According to the ultimate truth neither rūpa nor nāma has those characteristics.
OP: Can we say "a moving mind", "mind is located inside the body", "after the death, mind leaves the body and step into a new body" ?
No, neither rūpa nor nāma can move. They arise, exist, and cease then and there. New rūpa may arise at the same place or nearby. They will also exist, and cease then and there. This is called "Deshāntarotpatti".
OP: Can we imagine "How mind looks like" ?
No one can see mind with eye consciousness. So you can't imagine "How mind looks like". But you can understand the behaviour and characteristics of your mind.
OP: Are there any similar characteristics between Nama and Rupa?
To answer your original question above, yes, there are similar characteristics between rūpa and nāma. Both rūpa and nāma are conditioned. All the conditioned things share three common characteristics. They are anicca (impermanence), dukkha (suffering), and anatta (not-self).