Does intramolecular hydrogen bonding occur with carbonic acid and geminal diols? Is an intramolecular hydrogen bond possible in such compounds?
What are the requisites to have intramolecular hydrogen bonding?
Is this possible?


Probably not possible. An elementary explanation would be "too much ring strain."

https://en.wikipedia.org/wiki/Ring_strain


  I'm a bit confused: What are the requisites to occur a intramolecular hydrogen bonding?


5 and 6-membered rings are more favorable. As a matter of fact, beta-ketoacids, when warmed, readily decarboxylate. Why? The intermediate to decarboxylation is stabilized through hydrogen bonding. 

Note the 6-membered ring in the picture below.