Does intramolecular hydrogen bonding occur with carbonic acid and geminal diols?
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.