Since Middlesex no longer exists, and hasn't for 50 years, but has been subsumed into London, the answer is yes. You can send a letter from anywhere to anywhere provided you pay the postage.
Yes. In fact, Middlesex was absorbed into London by the 1963 London Government Act. It now only exists as a historic county.
Providing that you write the address properly on the envelope and fix a valid stamp then you can send a letter to anywhere.
Of course. Almost the whole of what used to be Middlesex is IN London anyway.
yes.
you can send a letter from/to anywhere
no. illegal