Applicable to all of your questions: the only way you can do any of this work is to make a Part P Building Regs application. Or use a Part P certified electrician. That's the law.
1) Having the type of cooker isolation switch you have is not a problem per se; having other wires hung out the bottom of it is a problem. I am not aware of a Reg that says the switch can't be in a cupboard.
2) Yes
3) 6 mm. squared is usual.
4) It is usual to have the kitchen sockets on a separate circuit to the rest of the house but not a Regulation - it also depends on the size of the house and the total number of circuits.
5) Yes - more than adequate unless the house is a palace and the total cable length of the circuit is absolutely massive.