That's exactly how the microwave thermal switches work, I've had them fail before - Most are supposed to be self-resetting, there may be some that fail permanently. I suppose you could add a fuse or a breaker in the junction box if you're so inclined and know how to do it. I'm not sure what the advantage of flipping the motor over would be. I would assume the motor provides adequate power to the saw, and I guess a washing machine motor ought to do a reasonable job- they are fairly heavy duty, and made for a pretty long duty cycle. I can't see anybody running a saw for the equivalent amount of time.

Do you know where it goes? Is it possible that this used to be a three way switch but the other switch was removed at some point? If the second black wire has power when the switch is "off" (I'm assuming you mean 'down' since a 3-way switch isn't on/off ... it's up/down), but nothing turned on when you flicked it "off", then I'd say it's safe to just cap that black wire and push it to the back of the box. It isn't being used for anything anymore.

Presuming the OP and his/her family will be the only occupants of the home, it is their choice and their responsibility whether or not they overload circuits and put 30A fuses in 15A holes. I think we could be spending time and energy a lot more wisely by recommending that they not, rather than trying to scare them by describing what SOMEONE ELSE might do. I agree with brickeyee's assessment except for the slight possibility of insulation damage leading to arc'ing where a k&t conductor passes through a device box. The arc current may be low enough to not blow a fuse, while still generating enough heat to start a fire. My current home is a mix of almost every wiring method ever used. My lights and one livingroom outlet are k&t, the kitchen is partially modern NM, partially cloth. Most of the remaining receptacles are cloth, but a few are BX. I know what's what, what goes where from where. The wiring to the major appliances, fridge not included, has been updated - the rest is old. This is BETTER condition than my last few homes. Not one of them has torched itself yet. I am IT for a local call center. I have my own test system set up here with three rather-serious servers in a rack in the livingroom closet and six PCs set up around the house. A prior hobby was DJing so I also have quite high-power amplification. My TV is a Sony trinitron cube monitor which isn't exactly light in its power consumption either. I also have two window ACs (the larger of the two being 12.5K BTU)... The point? Your average family, at least in my region, uses a crapload less power than I do, and provided they're not stupid about it (over-fusing circuits), probably doesn't need to be freaked out over some wiring not being the latest and "greatest".

What you are missing is that if there is no ground wire in the existing cable, there will be no ground for the circuit and any extension of that circuit. The new cable's ground wire can therefore be ignored because if it were connected it would not be doing anything. Connecting it would only mislead someone who was working on the circuit later. The purpose of the ground wire is to trip the breaker if the housing of the exhaust fan came in contact with the wiring and would shock someone who touched it. It is unlikely that someone would be touching the housing unless there is a light in the fan housing. I'm not sure what the electrical code says about extending a non-conforming circuit to a new fan but I doubt it is allowed. Of course, it is also likely that only a licensed electrician is allowed to do this work. In any case, if the installation caused a fire it is unlikely you would be insured if there was evidence the fan was not installed by a previous owner. Also, if the new junction box is metal you must use cable clamps where the cables enter through the knock-out holes. The box not only provides isolation of the connection but secures it so it can't be pulled apart. The cable must also be stapled to the framing at certain intervals; it can't be lying loose in the attic. 2 wire ungrounded non-metallic sheathed cable is rare in my area. Post knob & tube, home wiring was metal armored (AKA "BX") and the metal provided a ground to the metal boxes although it was not always reliable for long circuits. In the 60's an aluminum strip was added inside the cable to improve the continuity of the ground. Non-metallic (plastic) sheathed cable (AKA "Romex") became popular in the 50's and in 62 the electrical code made a bare ground wire mandatory for all branch circuits. For your wiring to have only 2 wires and no ground it would probably have been installed in the 50's by someone who didn't want to use BX cable. But this is not all bad because the insulation on BX wiring tended to crumble when exposed to air and is more dangerous than any other kind of wiring wiring. For any further help you should post photos of the original cable and the main panel with the cover off. Tripping the main breaker is wise but NEVER assume a branch circuit is dead without using a voltage detector. If a breaker can be turned off, it can be turned on again by someone else. Always put a note on the panel. A 120v wire can stop your heart instantly. A voltage detector is the smartest $10 you will ever spend. Here is a link that might be useful: voltage detector