As to (1), from ask.ba :-

"Responsibility for children travelling alone

Question
Responsibility for children travelling alone on British Airways flights

Answer
British Airways will only accept responsibility for children travelling alone between the departure and arrival airports. This refers to children from 5 years old up to and including children aged 12 years old travelling on a single-leg flight (the aircraft does not touch down anywhere) which is under 4 hours in length; or children aged from 6 years old up to and including children aged 12 years old travelling on multi-leg flights or those over 4 hours in length.

The following notes are also important:
Once a child has been accepted into the care of British Airways, the child will be escorted at all times e.g.toilet/shopping. If there is no escort available, the child will not be permitted to leave British Airways care to pursue leisure activities.

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Prior to a child travelling alone on a British Airways flight, we will need to know the following information for the child/children: ...

Please click here for further information about children travelling alone on British Airways flights.

Please note:Children are classed as those who have not reached their 12th birthday. If the child has reached their 12th birthday they are permitted to travel unaccompanied.

Not sure about the lounge question although I do recollect there being a min age (something like 16) for solo lounge access. Check ask.ba on the ba.com website. Whatever the rules, if he is presentable and well behaved he is unlikely to be turned away if he has a J ticket.