I got quick question, I am apply for a Chinese f type Visa, I have done this 2 times before, as I have done a internship and studied in china

hello
I am going again to Shanghai for an 6 month internship with my girlfriend who was also with me there,

the question I have is that I am currently in Lativa and the consultant here doesn't want to issue me one as I have a UK passport, would It be possible for us to get a double entry 180 days F type in Hong Kong??

also is there any special information that my host has to put in the invitation letter for us to have double entry? or do we just pay the extra and tick the box on the forum?

I also read somewhere that because I have had 2 F in the past 2 years I can get a multi entry, is this true?

thanks a lot for your help
james