Nothing. The sender needs to tell the recipient what their state is via some communication method. The recipient needs to accept that state before a timelock expires. If they don't, the state transition never really happens.

In theory yes, similar to how lightning does it, but I haven't implemented that yet.

Hedgehogs are known to be rather fast and they are also cuddly and cute. There are also lots of puns you can do with it, so if people want to build stuff on top of this, there is lots of room for naming things creatively.