Licence verification does indeed take place - it usually occurs from an airline of an external country who reaches out to TC and requests licensing validation.
Chinese carriers did it for me.
Im not sure who they contacted but I would start with TC 4900 young street in Toronto They will know something about the process.
As for flying time most of it is updated when we do our medicals we are to fill in amount of flying in last year etc... so there is a meager way to track it but technically the letter only says you officially have the licence.
WJP