Aveline, funeral services are public events (unless specified as private) so the date/time is communicated - and it's only the wake that needs an invitation.
That's usually for close friends and family only - so it should be fairly straightforward to estimate numbers. I think your friend is stressing because she's unaware of the usual conventions.
Several hundred people came to my husband's funeral - many work colleagues, friends from snooker and golf, neighbours, hospital staff and cousins - many I had never met.
Still, the 'after party' (as he'd called it, when planning the event) was for about 30, and that was quite enough. We had a buffet, so knowing the numbers wasn't vital.