Do they offer soy milk or non-dairy milk to substitute cows milk in their drinks?

Yes, i think they offer almond milk or soymilk

I ask them to use coconut milk instead of cow milk & they’ve always swapped it out. A lot of the drink powders do contain milk powder, so be careful with the milk teas if you’re allergic. The fruit options might be safer.

Yes

They do.

They may, I'm not sure, BUT... Make sure the person taking your order can communicate well enough to understand what you want... This may be biggest challenge.

I think so.