The underlay is for sound-proofing purposes, so it's really up to your judgement on what you want to replace it with. The only benefit that I can see that the original underlay has over some other generic stuff is that it has a spashproof top which will stop most of the water from general use (i.e. from your shoes) from soaking through the carpet and directly into the underlay. I guess it would be easy to create something similar.
I got mine from a MK3 and cut it to roughly the right size.
Check the floorpan for rust, treat any you can see, and make sure it is uber-dry before you start building it up again. I let mine dry over a couple of days, and sprayed some waxoyl in there for good measure to tease out the last of the moisture and matrix-proof the floorpan for the future

I'm guessing the really big flap you're referring to is the temperature mixer on the front of the heaterbox? The control levers are connected via cables to some gearing on the left hand side of the heaterbox, which controls the flap. If anything on there looks broken, I'd look at replacing the whole heaterbox. Anyone breaking a later Mk2 should be able to supply one for a reasonable price, though as you now probably realise, it's a bit of a ballache to get out. If you do replace it, make sure you replace the heaterbox and controls as one - once you disconnect the control cables, you're going to struggle to get them lined up properly again.
I really don't understand why a previous owner cable-tied it shut, unless it was flapping around. Even so, if you strip it down enough to get to the flap, then why not replace the thing?? What's the point in doing a half-arsed job, when only it only takes a little more effort to do it properly??