I would like to get to know you better my...


Espero haberte sido útil! :-)

English would almost never use as formal a register in writing letters as Spanish does. additionally, canned phrases such as this first one are rarlely used in English, at least not in the same way. "i hope you're doing well" gets the whole idea across without expressing the obvious fact that the person has received the letter (which they obviously have or they wouldn't be reading it)
(other options: i hope everything's going well for you. i hope you're doing fine. i hope things are going well for you. etc.)
anything like "i hope you're well when you receive this letter" is very stilted, and wouldn't almost never be used in modern english. "I hope this letter finds you well" is a common phrase in english letters, but it too is very outdated, and in an informal letter such as this, would not be used.
as for "quisiera conocerte mas mi..." depending what follows, "I'd like to meet you, but my..." etc. or "I'd like to get to know you better my..." etc. would work great.

I agree entirely with my colleague that this is a very common way of greeting someone by letter. I have omitted the 'happy' as it was not present in the Spanish.

Gillian