Yes, soya milk is fine for most cooking or sauces. Probably best not to use sweetened soya milk or vanilla flavour etc, would make a strange tasting quiche.
Depends on the quiche recipe, you could use blended tofu instead. That could give a thicker/creamier texture.
For coffee, it depends on what sort of coffee, and what sort of soya milk. Some curdle, some don't. Instant coffee is much more likely to curdle than proper coffee.