Main outdoor breaker is ONLY 100 AMP but total of Breakers AMP on internal panel is 165 AMPs.
Synopsis: The sum of all the branch circuit breakers is a meaningless number. 

The main breaker will "trip", or "flip off" as you say, when the current (amperage) load well exceeds it's rating for a predetermined amount of time. Meaning a breaker does not trip when the load is 1 or 2 more than the rating. The "continuous load" on the panel should not exceed 80%. In a residential application this is a hard number to pin down though.

As to your sub-panel question, a load calculation is the only accurate way to tell if your service is adequate to support any new loads on the service.