Fallout – Are legendary and unique weapons with same description identical

No, true unique versions don't exist for every weapon but you can find legendary versions of pretty much every weapon in the game except for those special unique ones like the cryolator or alien blaster.

I already watched a video of someone modifying a unique weapon. Specifically, it was the unique Laser Rifle Righteous Authority, which is obtained from a quest, so yes you can modify the unique weapons to your heart's content. The unique weapons all get bonuses for their stats that they keep regardless of how you modify the weapon in the case of Righteous Authority. Critical shots always do double damage and crit meter fills 15% faster. The nice thing about this is you will be able to change the unique weapon to fit your play style, meaning the unique weapons will be far more useful then in many other games I have played where out of all the unique weapons I only use 1 or 2 because those are the only ones that fit my style of play.

No, there is no way to see what the stats of each companion's default weapon are as there is no way to get this weapon to show in their inventory (unlike their clothing/armor). Even if you equip them with another weapon, their default doesn't appear in their inventory.