The only things in the component definitions for Mercenaries which might limit a component to one per game are the <Type>Mercenary</Type> and <PlacementType>Mercenary</PlacementType> tags, though I'd be far more inclined to believe that whatever limits the mercenaries to one-per-game has to do with how the game handles purchasing things from the Mercenary Bazaar rather than being anything to do with any tag in the component definitions.
I don't really know why Stardock bothered with limiting the mercenary components to one-per-ship; the mercenaries use static blueprints and the components are not available to the player in the first place, so there's no way within the game for more than one of the components to be placed in the first place.
You could include the ship you want with everyone starting ships.
Including the vessel among the starting ships and not permitting the player to design new ships with said "unique" component means that you're either going to provide the player with an insanely powerful starting ship or the unique component becomes worthless in short order because the ship with the component cannot be upgraded to keep pace with player-designed ships in speed, firepower, defensive strength, or whatever else it needs. The only exception is if the unique component provides a benefit unrelated to ships, but at that point it should probably be a player-unique or galaxy-unique structure rather than a unique component.
I've seen that some components are 1 per ship, but just wondering if it is possible to limit a component so that you could only field one ship at a time with a certain component?
There is one way that I can think of, though in order for it to actually work you'd need to turn off strategic resources in map generation. You can make components require strategic resources and you can make buildings provide them (at least, so I assume; never tried it, but since buildings can require strategic resources and most fields in the XML accept both positive and negative numbers without breaking the game, I'd expect that you could make a building provide strategic resources), so if there are no strategic resources on the map and you have a player-unique or galaxy-unique building which provides a specific (set of) strategic resource(s) and then have components require those resources. This would mostly work, though if you used player-unique structures to provide the resources then conquering such structures built by the other factions would allow your empire to build additional ships using those components, and there might be some issues with the computer being dumb enough to trade its resources to you long enough for you to build additional ships, or with the computer wasting the resources on something other than the special components.
If the XML allowed the creation of new strategic resources, I'd be inclined to make a special one for each empire-unique component I was adding and then see if I couldn't have one of each such strategic resource added to the faction definition (which would avoid issues with being able to capture structures generating the resources, though not with trading the resources away), but sadly as far as I know the game doesn't permit the addition of new strategic resources.