The Circle Line
Unfortunately this answer is wrong! According to Transport for London the only tube line to connect all London Underground lines is the Jubilee Line.
jubilee
Presumably you mean the London Tube? If so, it is the Jubilee Line (silver).
Yes, parts of every underground line on the tube network use stations that are also used by the circular line, and are therefore connected.
The Circle line connects with all TFL "underground" lines. It does not (directly) connect with the Emirate Air Line (the cable car link between Greenwich and the Docks) and the London Overground (an "outer" circle line around London). (Both of these are marked on the Underground Map, the latter [definitely] operated by TFL.)
The London Underground did give the East London line to the London Overground to ease its traffic.
On the London Underground map, the Circle Line is coloured yellow.
Central Line
Yes, that is correct. You have answered your own question.
You need to get the Northern Line to Leicester Square and then the Piccadilly Line to London Waterloo.
Hammersmith & City line
Jubilee Line.
It's on the BAKERLOO Line.
Hammersmith and City.