Currently, you're in the top three in the Empire for most dwarf rep, after the Elector Counts of Ostermark and Averland. That may chance depending on events in the coming Elector's Meet.
Dwarf Rep is both a rating and a currency - having 15 points means that every dwarf that meets you is going to know you as
Dawri. This is a word that means 'as good as something can get without proving itself over a few decades', or, literally, 'dwarf-like'. You helped Zhufbar and Karak Kadrin strike out some very old grudges that otherwise would have been very, very difficult to set right, and that's no small matter.
You can spend the currency to represent calling in favours, but the rating won't drop unless you actually act against the interests of dwarfkind. I'll probably end up recording it as '15 rep, 15 unspent' or similar.
- Have them send trainers for the watch
One point for skilled but common in dwarf society (Miners), two for specialized units (Rangers), four for true expertise (Ironbreakers), eight for hero-level instruction.
- Have them send experts to assist in setting up industry for turning that saltpeter into quality gunpowder
Five points.
- Personally tutor Mathilde in mundane fields (combat, tactics, mathematics, history)
Same scale as the trainers, depending on the quality of the teacher.
- Or in Khazalid?
Four points.
- Let Mathilde move into a dwarf hold and live there
If you promise to refrain from spellcasting inside the Hold, and would be willing to live in the bunkhouses, your rep would be enough.
- While conducting magical research?
Four points, and you'd have to work out a way to have a laboratory far from the populated parts of the hold.
- Send a force to assist in a campaign against someone they already hate
If they've outstanding grudges, and you're in a position of power in the campaign, and they've got the forces to spare, your rep would be enough.
- Or that they don't care about?
Impossible.
- Have one of their experts consult with Mathilde on vaguely appropriate magical matters (enchantment, Qhaysh Juice study)
Same scale as the trainers, with a 12 if you want to briefly collaborate with a Runelord.
- Provide her with/sell her enchanted equipment of their make
Eight points to commission something from a runesmith; you'd specify the item but they'd decide the details, since it would be a gift rather than a purchase. (yes you spend dwarf rep but that's an abstraction, it would be a gift)
- Or mundane but high-quality equipment, such as pistols?
Your rep means they'll sell them to you, or you can spend four points to commission something.
- Or have an expert collaborate on an enchantment project with her?
Would need to be arranged personally with the expert, but two points could get you an introduction and their ear.
- Help Mathilde dig or renovate an underground base somewhere
Two points to dig, five to renovate it so that it'll last at least a thousand years. It would cost more to renovate it to a lesser standard.
- In total secrecy?
As above, and you provide the ale.
- Assist in construction of some key project, such as a bridge, road, or fortification
If you mean consultants, same as the trainer scale.
- Or just do the whole thing?
Would need actual payment, and the cost would be commensurate with the craftsdwarfship, but a point per project would open the door to commissioning the work.
- Share maps, information, and general intelligence on the things that dwarves know about events in the world but Mathilde doesn't
Too vague to say. If you mean skaven, say skaven.
- Provide her with letters of introduction testifying to her skill and trustworthiness?
Two points, but it would be fairly curt.
- Or a temporary companion/aide in diplomatic matters?
As per the trainer scale.