Unless I'm missing something in your explanation, using the 2/0 AL wire doesn't seem to be a problem, except that it's AL and the unit does not specify AL. What will probably be simpler than running all new wire is to just get AL-to-copper splice connectors.
And in response to:
if I run two separate circuits/lines, do I need to tie together to the (2) 240 volt 2-pole breakers
No, you don't. If the heater circuit trips, you'll just lose your heat. And if the air handler breaker trips, it will shut off the heater strips. So no problem there.
In response to your update:
If the breaker is visibly damaged, then replace the breaker. If you decide to keep the AL wire, then make sure the breaker is rated for AL. Again, replacing the breaker will be cheaper than running all new copper.
A partially melted lug is a bad sign. You need to get an evaluation from a professional.
Having two breakers is still not a problem. If breaker for the lone heater strip trips, you get reduced heating capacity. If the other breaker trips, the air handler will shut off the other heater strip automatically.
Yes. Three lamps in series will work, provided they are reasonably well matched in terms of current flow and resistance. Automotive bulbs are actually meant to run on 13.8 volts, which is the voltage of a car's electrical system when the generator is running. That gives you about a 20% margin between bulbs on 32v. Can't see a problem. If one of the bulbs blows, all 3 series bulbs will go out. The other two are not blown. If you can't get 3 that match, replace all 3 with another kind.
Another option is to look at LEDs intended for automotive or RV use, but rated for a range of voltage, e.g. 12-30VDC. This multi-voltage rating means they have an electronic switching power supply inside, which adapts the incoming voltage to the constant current the LED needs. Same concept as those 100-240v laptop power supplies, or 100-277v fluorescent ballasts. They commonly specify 24 or 28 VDC as their max voltage, but there's a fair chance any particular brand will work fine on 32V.
Yet another option is to get a 12V DC power supply to replace the 32V power supply. 12V DC switching power supplies are common thanks to the popularity of custom LED lighting. You would not need to rewire; simply leave the lamps in parallel. However, since voltage dropped by a factor of 3, current will increase by a factor of 3 (assuming you stay with incandescent bulbs of the same brightness) - so make sure your wires are thick enough. I would actually recommend also converting to 12V LED at that point, which draws much less power and solves the wire-thickness problem.
Historically, electric streetcars/trams used five 120V bulbs in series powered by the 600V DC trolley wire. 600VDC arcs like crazy, so the bulbs are special "transit grade" types designed to snuff a 600v arc when they burn out.
Resistors are a bad idea. Railways do that too, commonly for headlights, and it's a pain - the resistor must be matched to the bulb. Changing bulb types requires recalibrating and often redesigning the resistor. Also, resistors run at spec have a 700 degree F surface temperature - dust accumulation or a bit of paper could start a fire. Even if you wildly oversize to bring the temperature into safe range, you still have to deal with the waste heat.
By the way, last I was in an auto parts store, they wanted $6 for a 2-pack of bulbs. Don't pay that. Online, they are much cheaper.
32v is a largely obsolete voltage once used in railways. Bulbs are getting very hard to find. If it has anything to do with a pool, I would switch to 12v.
For incandescent lights, heaters and other resistive loads, you don't need to worry about AC vs DC. AC voltage is labeled based on the DC voltage it behaves like: to a resistive load: "32VAC" is that voltage which will make the bulb the same brightness as 32VDC.
Best Answer
I know you've seen LED replacement "bulbs" that screw in, and you know those fail. What is failing isn't the LED. It's the conversion power supply which converts 230V to 3V for the LEDs, which tend to be built very cheaply. You could fix them, but it's not worth it. Don't let that scare you away from LED tech. The actual LED emitters proper have an extremely long service life. They will not burn out, probably in our lifetimes.
So anytime you're homebrewing a lamp, the right answer is to use LEDs because LEDs use low-voltage and run cool. There's a quasi-standard for projects like yours, to use 12 volts DC -- the LEDs won't run directly on that, but there are lots of ways to buy 12 volt LED modules that simply contain three LEDs and a resistor. The resistor will last as long as the LEDs.
To power that, you use a common, commercial off the shelf 230V-12V "wall wart" type power supply, which is listed by the relevant safety agencies - BSI, TUV, UL, whoever you use. (CE is pretty worthless when dealing with China). That means you are never touching mains voltage. An electrical short could still cause a fire, but 99% of such fire-starters are arcing faults across open connections, and 12V doesn't really like to arc. All the "failable" electronics are in the wall-wart, all the rest is wires, LEDs and resistors. The wall-wart will be what fails, just swap it.