a) Break of journey not allowed at an intermediate underground station if your ticket include cross London? Or rather you can break, but have to resume at National Rail kick off point
That's how I understand it (again, on a non-advance ticket). Any station apart from these in the list here and you've got to pay (oyster, contactless, whatever) to resume the journey (or walk to the intended station of course):
http://www.nationalrail.co.uk/times_fares/ticket_types/46587.aspxList of London Underground and DLR▸ Stations between which single/return tickets valid for travel ‘via London' may be used - subject to route of the through journey being made.
Aldgate, Amersham, Baker Street, Balham, Bank, Barking, Blackfriars, Blackhorse Road, Brixton, Canada Water, Cannon Street, Charing Cross, Ealing Broadway, Edgware Road, Elephant & Castle, Embankment, Euston, Euston Square, Farringdon, Finsbury Park, Greenwich (DLR), Highbury & Islington, Kensington Olympia, Kentish Town, Kings Cross / St Pancras, Lancaster Gate, Lewisham (DLR), Limehouse, Liverpool Street, London Bridge, Marylebone, Moorgate, Old Street, Paddington, Queens Park, Richmond, Seven Sisters, Shadwell, Shepherds Bush, Southwark, Stratford, Stratford International (DLR), Tottenham Hale, Tower Hill, Upminster, Vauxhall, Victoria, Walthamstow Central, Waterloo, West Brompton, West Ham, West Hampstead, Whitechapel, Wimbledon, Woolwich Arsenal (DLR)
(I sorted their table into alphabetical order in the quote)