How Can 3 Wire Wall Switch Control Fan And Light

Question

I have a wiring configuration that appears to allow for a unmarried switch piece that controls a ceiling fan AND 3-fashion switching of a ceiling fan low-cal (at that place'south another light switch on the other side of the room that seems to pair with the iii-way light switch).

What is currently hooked up in this spot is just a fan command (with a red and white wire), which controls the current lightless fan. Withal, there is another loose crimson wire in the box that goes hot with the low-cal switch across the room, and so I'm thinking I can replace the fan with i that does have a light that I can control from both locations.

My primary questions are:

Does it seem similar I take correctly deduced that I can add together a fan with a low-cal in this style?
Is there a slider/switch combo I can buy that both controls the fan and acts as a three-way light control? I'm having trouble finding ane, but might not be searching correctly

Bonus question: the fan is on a very high lofted ceiling - and some have said having a calorie-free at that place would get annoying when bulbs need to exist inverse (pretty much would need to rent a 12-ft ladder), however I think the extra lighting is worth it and bulbs these days last a long time… whatsoever thoughts or experiences? :-D

Thanks!!

UPDATE: calculation photos of the two boxes. The larger box includes the current fan control hooked up on the very left, and the smaller box is the one wired for 3-style. The middle switch in the large box is a single-pole for a hall light and the one on the right is a 3-way switch paired with a different switch for another hall light. The two wires hooked up to the fan control (ane cherry and one white) are both hot (per my contactless voltage tester): the white wire is coming from the cable on the far left (forth with the loose ruby wire that goes hot when i flip the paired 3-fashion switch across the room, a ground wire, and a black wire that'southward joined with the other black wires in the box); the red wire is coming from the second cable from the left in the box, forth with a ground wire and white and black wires that are joined with their other similar-colored wires in the box.

UPDATE2: adding a photograph with more than item of the larger box and the wires labeled - source cables are colored in yellow and the corresponding individual wire terminuses in green.

UPDATE3: adding a chart of which wires are hot in the 3-style switch box and the larger box (just those on the left side: the reddish and white hooked up to the fan command and the other loose red wire), based on configuration of the three-way switch I take installed (whether the crimson or the white wire is wired on the same side of the switch as the black common wire, and which position the switch is in). Checkmark=hot. Maybe this isn't supposed to be a 3-way switch?

larger box 3-way switch box large box labeled 3-way switch chart