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When should you see outfits that require a minimum ship size/class?
At all times - to see what's available and where.
Anything that can be purchased without completing a mission first should be available at any time.
If you had a large number of outfits I could conceive that reducing clutter would be beneficial, but for the most part it would only cause confusion and players wouldn't be able to make note of where to go once they bought that nice big warship that they want to deck out now.
Another reason to only show ship/class-specific outfits would be if you dispensed with the use of tech levels and sold everything everywhere.
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When should you see outfits that require a specific ship?
At all times.
This depends.
I say at all times if it's for use with a ship that you can buy without completing any missions and if it isn't immediately obvious that the ship has it or can use it. A shield enhancer exclusively found on or made for ship X would be an example of an item that wouldn't be immediately obvious a ship has or can use.
It probably should be invisible if it is a special weapon that only a certain ship has and is clearly visible on the sprite the UE Fighter's gatling guns, for example.
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When should you see outfits that require a specific faction?
Only when it can be used.
For the most part, players will realize there's something cool to be had by seeing a factions' ships in action. I think part of the fun when playing for a faction, even if it is an allied faction, is actually "unlocking" technology. I also see no reason why a faction, friendly or otherwise, would show you their sensitive technology unless it was a trading guild or somesuch organization who would not be adversely affected by allowing regular citizens to inspect their designs.