I have a question about our trip to Cgernobyl. Can we arrive to checkpoint Dytiatky with motorcycles, park them near/inside the checkpoint and join some kind of group with other visitors?

You can do that, but you need to apply for the tour beforehand. You cannot just come and join any passing group. You must have permissions to enter the Zone and other papers.

If I have permission to enter the Zone and other papers?

You must book a tour anyway. You will not be allowed to join some tour at the check point. You must be in the list of the group that you want to join. If you are not in the lists the police will not let you in.

If I listed in a group list in advance BUT arrive to the checkpoint with motorcicle?

You can arrive to the checkpoint with your motocicle, but you will have to leave it ther and get on the bus with other tourists.

Sposibo!