No, it is not required. You can remove it and splice the heater hoses together.
the vacuum hose connects to the airbox
near the fire wall where the heater hoses enter
Check the vacuum operated valve at the hose going to the heater core.
Fixing the heater contol valve is very simple, however, what i might say could be totally different than what you need. I have a 1987 Jeep Cherokee Pioneer 4.0 and my heater control valve went bad and started leaking coolant like crazy. This is a very common problem with these older Jeeps. luckily, it's an easy fix. What you have to do is go to your local parts store (Schuck's/Checker/Krager, Napa, Auto Zone, O'Reilly, whatever) and ask for a heater control valve for your application (year, make, model). then it's just a matter of locating the valve (between the coolant reservoir and heater core) undoing a couple hose clamps, taking out the old one and putting in the new one. very simple. I hope this was helpful.
No.
It goes to the ac/heater control head.
A 1993 Jeep does not have a transmission modulator valve.
No
Idle air control valve found on Tue backside of throttle body.
The transmission solenoids are inside the transmission on top of the valve body.
A 1999 Jeep transmission does not have a modulator valve.