Creating a Domain Trust between Forests

I have two domain forests. One resides in an office in the US. The other is in an Office in the UK. I would like the users in the UK to be able to authenticate and access resources in the US forest and the US authenticate and access resources in the UK forest. Both networks are not connected.

My questions:

Would I be able to create a trust between the two forests or am I misunderstanding the whole trusts relationship concept?

If I can create the trust, would I need a connection between the two forests in order to replicate the AD related data back and forth between the two forests?

Thanks, Andrew