I want to say the limit is 42 but that may depend on what version of the code your municipality is using. The manufacturer of the panel will also limit the number of circuits. Check the label for the number.

The combined amperage of the individual breaker will always (or almost always) exceed that of the main breaker. You typically don't use everything at once but there are calculations you or your electrician can perform to see if you have a large enough service.

The limit is what the panel supports. It used to be code to limit the maximum OCD's to 42. Some panels accepted less. Some only accept tandems in certain slots to prevent you from exceeding the old 42 limit. It should be marked on the panel somewhere.

The sum of your breakers can be more than the service size, which is ok. Load capacity can only be %80 of the circuit breaker size. The only thing you need to worry about is the actual load. This cannot be more than your service size, which may be what your electrician is talking about. He may think you are getting close to the service size.
Do a load service calculation to determine what the actual load is.

i used to think of it as 10a per pole per amp of main
150 a main 1phase 30 poles max
200 a main ditto 40 poles max
100 a main 20 poles max

"i used to think of it as 10a per pole per amp of main"

No such requirement exists.