The only things you need is a tap from Pink to connect to the B common wire and to flip the red and white wires on the Thermostat terminals: block.
Write down a big W above the T1 conn. and R below the T2 conn. label so you or whoever has to look at it later doesn't get confused.
Someone forgot a fitting
Normally, armored cables (like yours) are brought into a box using a fitting designed to clamp the the cable armor, grounding it to the box and also providing a strain relief for the cable inside. Your furnace installer didn't have that fitting on hand, though, so they simply shoved the cable through the hole and shoved a "redhead" ...
That looks good to me, the second "C" terminal connects to the chassis in the background of the photo so it most likely is equivalent to the screw-down terminal.
fitting a crimp-on fork lug to the wire would be another alternative if you really want to connect to the screw-down terminal.
A "freeze protection outlet" will let you plug a small heater (and/or alarm) in, and will only activate if the temperature dips to a dangerous level.
You can also use heat tape around any pipes that are likely to freeze, and insulate any pipes in under-insulated areas.
Finally, not all thermostats have an off setting. Compare this Honeywell thermostat, ...
In 1982 I had a somewhat similar problem while renting an upstairs apartment. Our downstairs neighbors had the thermostat in their apt and used to leave for the weekend and turn the thermostat down when they left. I investigated the furnace in the basement and found the wire to the thermostat, patched into it in parallel with a thermostat mounted on the wall ...