If we consider a disk $D$ with $h$ holes and $n$ punctures on the boundary of the disk, then:

Is there a uniformization theorem for such surfaces?

What is the condition on $h$ and $n$ such that we can consider such surfaces as hyperbolic surfaces?

What is the notion of mapping class group? How can we define it?

Is there an analog of the Fenchel-Nielsen coordinates for the Teichmuller space $T_{h,n}(D)$ of such surfaces e.g. just hyperbolic length functions?

If we attach a compact surface with genus $g$ and $m$ punctures to one of the holes, what would be the answer to the above questions?

Should we always resort to the notion of the double of such surfaces to study them?

Useful references are highly appreciated!