It's free: please see my reply to your second question. Transport depends on where you are staying but once in the City Centre, which is easily accessed by public transport (bus or Metro) everywhere is just a relatively short stroll.

There is no entrance fee for the Grainger Market. It's still a bustling retail market with a wide variety of goods on offer. Just browse, look around at the architecture and, who knows, perhaps make a purchase or two. Grainger town and the market are right in the centre of Newcastle which is very compact, so easily accessed on foot. The city's classical streets fan out from Grey's Monument, a statue on top of a high column and unmissable. It also sits on top of an underground Metro station. Hope you enjoy the sights.

Yes that's correct Liverpool has over 2,500 listed buildings including many Grade 1 and Grade 2* properties.