H24 ops is really not a viable option since the majority of maintenance and repair is carried out between 23.30 and 05.00 local. Try operating aircraft around large areas that have been closed for the night period.
Every other UK airport that is significantly H24 (Gatwick, Manchester, etc) manages this without issue.
Every other airport in the UK is also nowhere near as busy.
There is however huge current investment by TfL in the Crossrail project, one of whose key attributes is to provide a tremendous improvement in access from all across Central London, Canary Wharf, etc, out to Heathrow, improving both journey time and frequency. It's one of the biggest step forwards that Heathrow will have had for years, and TfL are fully in charge. It will also doubtless spell a longer-term end for the Heathrow Express rip-off.
Yet another reason why Heathrow is not closing in the forseable.
Paris has one hub airport at CDG and one point to point airport at Orly, much as LHR and LGW co-exist.
Very much so, except in one respect: number of rwys (4 parallel at CDG, 2 parallel at ORY).