Much depends upon your reading requirements and level of interest. The most authoritative overall account of Hadrian’s Wall is the book of the same name by David Breeze and Brian Dobson, now in its 4th edition, whilst the best detailed description of the monument is the 14th edition of Collingwood Bruce’s Handbook to the Roman Wall, edited by David Breeze. An accessible popular account is Alistair Moffat’s The Wall: Rome’s Greatest Frontier, but Hunter Davies’ A Walk Along The Wall should not be omitted just because it is more than thirty years old: good books endure.
This is more difficult to answer than for Bowness, as the lowest bridging point of the Tyne has always been Newcastle, whilst the lowest ford has traditionally been thought to be Newburn, some way upstream. It is possible (but not very likely) that the Romans discovered the river could be forded below the lowest bridging point.
Bowness represents the westernmost point at which the Solway could be forded, so extending the Wall to this point obviously protected it from being outflanked by those daring enough to attempt to cross the estuary (which cattle drovers regularly did right up into the 20th century). Its western flank was further protected by a series of towers and fortlets southwards along the Cumbrian coast as far as Maryport.
The philosopher and Wall scholar R. G. Collingwood began the scheme of numbering the milecastles from east to west, with MC1 some 1.15km (0.78 Roman miles) south-west of Wallsend fort (and thereby begging the question of whether there had been a MC0 south-east of the fort). Milecastles first gained their name in 1708, courtesy of Robert Smith, whilst turrets had to wait until 1726/7 for Alexander Gordon to coin the term.
Further reading: Birley 1961
This is a fairly meaningless question, except as an indication of how much material the Roman army would have had to acquire, move, and assemble. Assuming a volume of 10m³ for a metre of curtain wall (including parapet and consisting of dressed sandstone facing, rubble core, and lime mortar), and a mass of 20 tonnes for the requisite amount of stone and mortar, the curtain wall alone would have weighed in the order of 2.4 million tonnes over its 119km. With turrets, milecastles, and forts added in, this would probably come closer to 3 million tonnes.
Further reading: Hill 2006
Collingwood Bruce was the first to play the game of guessing the cost of building a present-day Wall. He came up with a total of £1,079,446 for curtain wall, ditch, and Vallum, allowing for the use of dressed stone. At present-day values, that would be between £80m (US$130m) and £770m (US$1.25bn), depending upon the method used to calculate inflation. A later estimate, this time for a concrete wall, was obtained from Laings by Hunter Davies (£80m in 1974, which would be between £620m (US$1.01bn) and £990m (US$1.61bn)).
So far as we know, the Wall cost nothing to build. The principal costs – materials and labour – were free for the Roman army and there is little likelihood that compensation was paid for the land acquired. In fact it might be argued that the project had a value in its own right as a way of keeping the army occupied.
Further reading: Breeze 2006