Is there some requirements (EASA or FAA) for additional life vests, and life vests for infants/children on-board estimation?
From the FAA's Flotation Equipment for In-Lap Children InFO (Information for Operators):
The FAA recommends:
Consider installing flotation equipment designed specifically for in-lap children.
We also find:
If an air carrier provides flotation equipment for in-lap children that is located or operates differently from the typical flotation equipment for other occupants, then additional information regarding that special equipment would be required in the briefing given to passengers.
Which means it will briefed to the passengers if it is present. (Too many if's.)
For the FAA, there is no requirement to have multi-sized flotation devices. Remember, seat cushions work well, and infants aren't good swimmers, but they also don't panic in water (maybe not all of them).
A reflex called the bradycardic response makes babies [up to 6 months] hold their breath and open their eyes when submerged in water, says Jeffrey Wagener, a pediatric pulmonologist in Colorado. (Source)
Cute video: Baby's first swim - underwater!
I'm only familiar with FAA regulations so I'll answer based on my knowledge of them.
For Part 121 operations (most commercial airlines), Section 121.339 of the FARs simply states the following:
(a) Except where the Administrator, by amending the operations specifications of the certificate holder, requires the carriage of all or any specific items of the equipment listed below for any overwater operation, or upon application of the certificate holder, the Administrator allows deviation for a particular extended overwater operation, no person may operate an airplane in extended overwater operations without having on the airplane the following equipment:
(1) A life preserver equipped with an approved survivor locator light, for each occupant of the airplane.
Therefore based on an interpretation of the regulations, there must be enough life preservers on board for all occupants of the aircraft, including children. I would assume therefore that airlines would always make sure to have enough and probably a few extras to meet this requirement. Given there are only a set number of seats per aircraft, airlines should have no problem doing this even taking into account children. You can only have so many occupants for a given flight.
From EASA Air-ops
NCC.IDE.A.220 Flight over water
(a) The following aeroplanes shall be equipped with a life-jacket for each person on board or equivalent individual floatation device for each person on board younger than 24 months, stowed in a position that is readily accessible from the seat or berth of the person for whose use it is provided: