You choose to do this after you have rolled the damage. Note that it says "you can spend 1 sorcery point to reroll a number of the damage dice ..." To be able to reroll dice, you must have already rolled them.
The Bard decides, but it is somewhat table dependent
As you've quoted for cutting words, the mechanic states:
When a creature that you can see within 60 feet of you...a damage roll, you can use your reaction to expend one of your uses of Bardic Inspiration, rolling a Bardic Inspiration die and subtracting the number rolled from the creature's roll.
When damage is being rolled, each type is rolled separately: different die, different modifiers, different functional rolls (but still counts as One Big Roll with regard to damage.)
The bard is seeing the damage coming in and using their mechanic to reduce the damage they want to reduce.
Other tables may differ
However, there is no written rule on this and a DM could easily say it was their decision. But I'd suggest to let the Bard bard and choose when and how they want to apply their mechanic.
But you have to pick one from somewhere in some circumstances (but not all)
Due to issues regarding resistance, vulnerability, there needs to be a mechanic where you choose which damage type to Cut. If there are none of the mechanics in play, then it doesn't matter - but if there are, you need to separate out the types otherwise you have no way to determine how and where to cut the damage.
Crossover damage
In the cases where the damage reduction is greater than any single damage type's value, then the remaining reduction would cross over to the other damage type. The bard has targeted Damage Type A, and the remainder (if any) goes to Damage Type B.
Best Answer
You should roll damage once for each beam.
Chapter 9: Combat in the Player's Handbook (and the Combat section of the Basic Rules) has the following rule under the heading "Damage Rolls" (emphasis from original source):
It uses the examples of fireball and flame strike, which are simple since they produce a single effect which hits multiple targets for the same amount and type of damage. In other cases like eldritch blast, magic missile or scorching ray which produce more than one ray, beam or projectile, each one deals the same amount and type of damage. In those cases each ray, beam or projectile only hits one target, even if more than one of them hit the same target.
Prismatic spray is an unusual case, since each beam produced can potentially hit multiple targets, and each beam does not do the same amount and type of damage - only the same amount (for those beams which have a damaging effect). However the multiple targets hit by a beam would take damage "at the same time" for the purposes of the rules (i.e. in the same instant/action the beams are cast), and the same amount and type of damage too, so it seems reasonable to roll damage once for each beam - i.e. each target hit by the same beam uses the beam's single damage roll. (For ease at the table, I'd have all the affected targets roll to see which beam hits them before rolling any damage.)
Prismatic wall is more straightforward - each layer of the wall is a separate effect, so the damage is rolled separately for each layer. This happens on each creature's turn, when they try to pass through the wall, so the damage would be rolled separately for each creature affected.
To answer your last question: both the sorcerer's Empowered Spell metamagic option and Lore bard's Cutting Words feature work as normal, though the former is a little ambiguous. Empowered Spell says:
This is the exception to the normal rule that you have to spend the points and use a metamagic option when you cast a spell, but it doesn't address whether it applies to a single or multiple damage rolls. I would say you could split the re-rolls across multiple beams, but it's not going to have a big impact on more than one, since at most you could re-roll five of the dice, and so it's true that it won't be as effective for prismatic spray as for a spell with a single damaging effect.
Cutting Words isn't going to make a big difference to the damage taken from prismatic spray unless the caster rolls really badly, but that's true of its effect on the damage rolls of most high-level spells. That fits the flavour of the feature - it makes sense a bard's distracting words would reduce the damage from a sword thrust better than they would a magical explosion.