Can I select the target for my spawn larvae with a hotkey and no mouse clicks?
You can't avoid to click, but you can click on the minimap.
If you select all your queens (say in a single control group) and cast spawn larva on the minimap, the closest queen will cast spawn larva on the closest hatchery to where you clicked.
This is another function of smart casting.
This isn't possible. The way you're doing it is likely the fastest you can hope for.