The amperage capacity of the main bus bars and the connection of the main breaker to the bus bars.
No, the breaker must have a rating of 125% of the wire rating, no more than that, so that's 125 amps.
I doubt if the 125 amp breaker will fit into a 100 amp box. This is due to the rating of the box only being rated at 100 amps. If this exchange could be made then the service conductors feeding the box must be upgraded to take the 125 amperage that the breaker will allow on the conductor.
You can reduce the breaker size because that limits the current that can reach the main panel. There is no safety issue other than the significant danger in an unskilled person changing out a main breaker.
A #3 copper conductor with an insulation factor of 90 degrees C is rated at 115 amps. Even though the panel is rated at a higher amperage it is the main breaker that governs the wire size.
% rate = 125/100 * 100% = 125%
125/100 = 1.25 = 125%
To convert a fraction to a percentage, multiply by 100 (and simplify) 100/125 = 100/125 x 100 % = 80 %
(100 + 125)/2 = 112.5
125 - 20% = 80% of 125 = 125*80/100 = 100