A sub panel must have the neutral and ground isolated. Panels come with a very long, rather thick (about 1/4 x 20) green bonding screw that connects the neutral bar to the can in the case of a primary panel. You don't get a neutral from your utility, you create one with that bonding screw.
Sub panels should be fed with 3 insulated conductors of appropriate size, and a ground that need not be insulated (but can be, if you want). So the first part of your question is, yes, that sub panel must be grounded, but the grounding conductor should be attached to the can using a ground lug, not by landing it to the neutral bar.
Sub panels must also have a fused disconnect, which means they need to be fed from a breaker, and there can't be anything else on that breaker. Don't double tap. You have two options here:
- Increase the size of the existing sub panel
- Put in a new double pole breaker in the existing sub panel and use that to feed your new sub panel. Land the circuits you had to pull out of the existing sub panel into the new one.
As others have noted, you need to watch your loads. If all you need are a few convenience receptacles or a lighting circuit, you should probably be o.k. (hard to tell with what you've given).
Either way, get an amprobe and look at what each incoming phase is pulling in your existing sub panel prior to doing anything. Make sure everything is on when you do. If it's only pulling 25 - 30A on average, you should be o.k. to add a small 8 circuit sub panel. Since it's directly in the line of sight with the existing sub panel, the new sub panel need not have a main breaker since the means of disconnect is right next to it.
A six to eight circuit sub panel runs about $80 without breakers, they typically start at 50A, but you don't have to feed them with 50A. You could feed it from a 30A breaker if all you want are convenience receptacles and lights.
Here is an amprobe being used:
(source: amprobe.com)
Do that on your sub panel first (one phase at a time) just to be sure you have room to add more. If not, you need to replace your existing sub panel, and an electrician is really your best bet there.
Another good thing to do is measure the draw of the circuits you'll have to move to the sub panel in order to make room for the breaker that will feed it. Obviously, you want to move the circuits drawing the least to the new panel in the end. Some re-arranging might be needed to make that happen.
Since this is a garage, take care what you connect to the sub panel. If you are going to be powering something like a compressor (or anything else with a decent sized motor), carefully consider the locked rotor amperage when determining the load. It will be printed on the motor.
Finally, if any of this sounds overwhelming, call an electrician. If you get into any kind of trouble, call an electrician.
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.
Best Answer
The answer is Yes you can add holes to the back of the box with a hole saw. Hole saws and slug busters are used by Electricians regularly for this. A 7/8" hole saw will provide the correct size for a 1/2" conduit, 1-1/8" will provide the correct size for 3/4" conduit and 1-3/8" is the size for 1" conduit. I use carbide cutters because they are a bit faster and last longer but a standard bi-metal hole saw will work with oil or cutting fluid if cut at a slow speed (full speed / no oil will will over heat the cutter and the teeth will dull quickly). Make sure to provide a little space from the wall of the box so the lock nut will fit inside the box. I usually cut my holes at the top or bottom sides so the wires look neat and installed in a workman manor that code requires.