#1 Does the grill need any assembling when it arrives?
Yes, mine arrived yesterday and as John O mentioned, minor assembly is required prior to use - affixing the handle covers and legs , but it only takes 10 minutes.
#2 How quickly can you pack it up after cooking on it and put it in the car please?
I really do not know and guess it depends how much charcoal you use. I only use my grill at home and not anywhere else. Personally, I leave the grill outside overnight to insure coals are all burned and unit is cool then clean grill and bring it inside. Perhaps closing all the vents may speed up cooling process but am not sure.
#3 Can you use small pieces of wood to cook with in this grill instead of charcoal?
You can use wood chips for smoke flavor but as for actually using wood as the heat source no. The gas and charcoal have different internal parts that allow and protect the housing.
You dump out the ashes by flipping over the bottom half-- ideally, into a steel container where there is little risk of embers burning the container. You can also line the bottom of the grill with aluminum foil and just remove the foil and ashes after it has cooled.
We use it on top of a wooden table on our deck and have not had any issues. We bought this for camping but like it so much that we use it at home as well.
#6 Is there a case you can get that fits this for traveling?
It will fit in a popup tote, like the carrying sturdy totes for groceries or utility tote.