More adjustments and extrapolations, I hope, than actual whole cloth house rules. Some things just aren't covered, or, if they are (for ships, anyhow) it's in Saltmarsh which has some different assumptions about crews, officers, and environment.

I'm extrapolating fire rules from Ghosts of Saltmarsh. Ship and weapons will each be handled a bit differently, as crewing between sea and space ships is handled differently.

Of course, some spells make all this moot, if used in a timely fashion. Prestidigitation is NOT one of them.

Sizes of fire will vary by cause. This probably means by which spell is used, so some examples:

DC 10: This is the best a Firebolt or other single target cantrip or low level spell will do.

DC 15: A Fireball could set off multiple small fires.

DC 20: Possible with a Wall of Fire. Certainly if a DC 15 fire grows.

DC 25: The max. A wall of fire the length of the ship could cause this, even after it's been dispelled. Certainly while it's present the fire won't be able to be extinguished. It will just restart round to round on the hot side.

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Hull on fire:
-IF you have a Captain designated, he or she may roll Int(Vehicle(Space))
-IF you have  Bard, he or she may spend one inspiration die to make an automatic success.
-A designated Artificer or other Carpenter may roll Str(Carpenter)
-A designated Healer or medic with Medicine training may roll Int(Medicine)
-Roll 1d20+1 per each remaining person that hasn't rolled but has training in Vehicle(Space).

Note that helmsmen may not roll or contribute to a roll. They are otherwise occupied...unless you go dead in space, then they may help a round later.

If you don't have someone to make a roll, that roll is considered a failure.

Rolf is your designated Medic.
Aelar is your designated Carpenter.

You have no Bard
You have no designated Captain.

5 successes: Fire is out.
3 successes: Fire is out after 6d6 more damage, but it is contained to just the hull.
1 or 2 successes: Fire is NOT out and 1d3 weapons catch fire, taking 6d6 damage each.
0 successes: Hull and 1d3 other weapons are on fire. All take 6d6 damage. Fire is growing.

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Weapon on fire:

Everyone on the Weapon crew rolls Int(Vehicles(Space)).
Ballista:
3 successes: Fire is out.
2 successes: Fire is out after 6d6 more damage, but it is contained to just the weapon.
1 success: Fire is NOT out (unless weapon destroyed) And hull catches fire, taking 6d6 damage.
0 successes: Hull and 1d3 other weapons are on fire. All take 6d6 damage. Fire is growing.

Mangonel:
5 successes: Fire is out.
3 successes: Fire is out after 6d6 more damage, but it is contained to just the weapon.
1 or 2 successes: Fire is NOT out (unless weapon destroyed) And hull catches fire, taking 6d6 damage.
0 successes: Hull and 1d3 other weapons are on fire. All take 6d6 damage. Fire is growing.

Note: a destroyed weapon is no longer an issue, but it's gone beyond hope of Mending.

Not actually a house rule, but canon, although kind of implied rather than spelled out.

Foci replace material components in a spell. This means that instead of a component in your hand, the focus is. It's not just a case of having it around your neck or in your pouch, you must take it in hand, as you would the component it's replacing.

What the book actually says is that the components are replaced by the focus and that you need a hand to access the components. 1+1=2, so you need a hand to access the focus (replacing the components the hand would normally be accessing).

A spell focus isn't set dressing, and you need a free hand for it, and you will have it in hand for any spell it's part of. That doesn't mean you can't keep in in your pouch, of course, as accessing an item from the pouch is a free action.