• Fashion guru Karl Lagerfeld let’s rip calling Adele 'fat' and Russian men 'ugly'
  1. What does "let's rip" mean here?
  2. Why not "let rip"?
  3. Can I put a comma before "calling", ie "Fashion guru Karl Lagerfeld let’s rip, calling ..."
Yes, it would be clearer with the comma. The apostrophe is wrong; the verb phrase is 'to let rip' , which here means to exclaim, to suddenly and candidly speak out. More generally:

11. let rip, Slang .
a. to utter a series of oaths; swear.
b. to speak or write violently, rapidly, or at great length.
c. to allow to proceed at full speed or without restraint.
Thank you VERY MUCH Mister Micawber!
Let me ask you one more question here (irrelevant to 'let rip' yet very important to English learners like me)...

"to allow to proceed at full speed ..."
Is there a clear enough rule that plainly "explains" in which cases an infinitive (with 'to') can immediately follow the verb "allow" (in the active voice). I have seen phases with "allow to cool", but never "allow to proceed". If you could explain this piece of English grammar in more detail (PLEASE!)