Yes, Teddington Lock is a good mooring point for exploring Teddington, Ham, Twickenham (Richmond, Kew, Kingston etc by bus) as Teddington_Lock says. Also mooring at Hampton Court, great for visiting the Palace. Mooring at Hampton too, with pleasant walking to Bushy Park, Hampton Court and buses...
Oh dear. Really sorry to hear that. Can you remember where and when it was? Any chance you saw the three letter club code? You should report it to British Rowing directly.
Most kayakists and canoeists carry their cards (ie licences) on themselves and will show them to the lock keepers. Many lock keepers recognise their frequent users, be they motorboaters, kayakists, canoeists, rowing clubs.....