It is extremely improbable that you would be allowed landside after being denied before. If the reason for denial are still there then you will not be allowed in.
It is your problem to arrange travel so that you do NOT get stuck with a long layover at the airport.
If you have been denied entry previously you would need to apply for a visa to enter the UK prior to your arrival even for a short stay. Visa on arrival is only available to those with no previous adverse immigration history.
Presumably your difficulties arise because you have a Police record. You should approach the closest British embassy or consulate to you in Canada and see whether it is possible to have a special visa stamped into your passport to enter the U.K. for the short period you wish to be here. Bear in mind too if you have had problems with the British authorities, the same may apply to the French ones
They may well think you are trying to enter the UK by booking a flight to Paris and getting off in London.
Looks like an uncomfortable sleep on a chair for you.
No. You stay in the airport.
