It depends what you mean by move around? You can go on and off the grandstand you have a ticket for, but if you mean can you gain access to other grandstands, then the answer is no. Also depending where you want to go some areas are not accessible unless it is to get to a grandstand you have a ticket for. Also around the circuit there are barriers to obscure the view so unless you have a ticket, apart from going up to the castle and hoping you can see something, you will be unable to see anything of the circuit.
Unfortunately not, you can only go in the grandstand you have tickets for although on Thursday you can sit in any seat as opposed to Sat/Sun when they are allocated seats. Unless you have a ticket for the other grandstands there is no access.
Historic is again grandstand only you have tickets for but not allocated seats, also only so many of the grandstands are open for the historic. But again circuit is closed off to general viewing.
I guess for what people are being charged for tickets for F1 they need to make sure you only view if you pay!