when is the personal starship weapon vale used?
Is it anywhere mentioned in the rules if a personal starship can intercept?
If so, I missed it. Just curious.
By "Personal starship", I assume you mean a "Character spaceship." I do not believe the rules use the term "starship" anywhere.
A personal spaceship's cannons are used in only one circumstance: When conducting a Spaceship Quest mission. Bonus draws for a Spaceship Quest mission are the sum of the evasion value of the pilot and spaceship (see rule 14.52) and the spaceship's cannon rating.
As a personal note, in my dozens of games of FitG, I have very rarly conducted any Spaceship Quests.
As for character spaceships being used to intercept, only military units can intercept or be intercepted. (See rules 20.0 and 20.2)
Of course, just because a personal spaceship can't be intercepted does not mean it is safe. Personal spaceships can be detected and attacked by PDB's and/or enemy military units.
I hope this helps.