Factory A/C & Heater Help

[big dump]

Turned on the A/C the other day and started getting a bunch of smoke from under the dash. Figured it was probably the electric switch on the controls so took it apart and found a few issues. First picture shows the burned up switch, second picture shows burned up compressor clutch wiring, third picture shows the high speed blower relay, forth picture shows the outside of the blower motor assembly with a mystery hose that's cracked.









Two questions, first of all, should the relay be mounted to the firewall, or is a remote ground sufficient? Secondly, what is the hose in the forth picture, and where can I get a new one? I haven't been able to find anything online about it, am I going to have to just get a plug fitting and new hose? Anyone know what it's called, and what it's for?

Thanks,