Assessing the adequacy of my electrical service
- 1100 sq ft, 2 bedroom, 2 bath, condo (circa 1988 in midatlantic region)
- Multistage natural gas furnace + 1.5 ton 16 SEER AC (circa 2012)
- Electric 50-gallon 4500w hot water heater (circa 2005)
- Electric range, microwave, dishwasher, washing machine, electric clothes dryer, refrigerator (all circa 2004)
- Typical electronics and other items - nothing out of the ordinary
- Meter to panel: 50' of ALCAN S STABILOY
AA-8000 SERIES TYPE SE CABLE STYLE SER TYPE XHHW CORS 600 VOLTS 3 CORS 2 AL 1 COR 4 AL (UL) 1987

There is no main breaker on the "125A max mains rating" panel. Would there be a limiting disconnect, of some sort, in the box next to the meter? I've never opened that box and I'm not very eager too, but is there another way to know for sure what the supply limit is?
Looks like a 100A service with the 100A four wire feeder cable.
The disconnect to the right of the meter will be safe to open. It must not be locked or sealed shut.
It should look like a miniature panel with a single 2P breaker.
As for the "interesting aluminum ground wire": I suspect it is original and it appears to continue toward the floor (can't see much of it). There are no electrical boxes below or close to the panel. There are copper water pipes in that wall and floor area, close to the panel. Maybe it connects to that? I suspect the water supply enters the condo floor near the shutoff valve which is about 30' away. If there is some other point where the water pipe is bonded I haven't seen it.
I suspect the aluminum ground wire is the service GEC (Grounding Electrode Conductor), but it is wrong. The neutral is required to be grounded at the first disconnect and the disconnect is adjacent to the meter. In addition, the GEC MUST connect directly to the neutral bus and not a ground bar.
I also see a couple issues at the top of the subpanel where multiple cables are entering the panel through raw knockouts with no connector. The Homeline breaker at the lower right in the photo does not belong in this panel, this is a code violation. Square D breakers are only UL Listed for use in Square D panels. If this is a Bryant panel the Siemens breaker at the top left is also a code violation. It doesn't appear to me that this place has ever been inspected by a competent inspector.
I visually confirmed that the disconnect breaker is 100A. I think I'm off in some respects and will try to improve my load calculation, but right now I'm landing in the 101A - 106A range (using optional method like worksheets I found). I'm confident that no breaker has tripped during the past 8 years. Maybe our usage pattern just doesn't create such a demand? Hoping to learn something, I got a Fluke 323 and measured current on each of the branch circuits (while creating loads of interest). Can those measurements be summed to compute total load?

Would the load on H1 be the sum of the loads on C1 + C2, C5 + C6, etc and the load on H2 be the sum of the loads on C3 + C4, C7 + C8, etc? Then, if either H1 or H2 exceeds 100A, the disconnect breaker would trip?
Breakers aren't instant. You could be running 105A through a 100A breaker for a few hours before it trips. 110A might take 5 minutes to trip. 120A might trip in a few seconds. (there are breaker trip curves you can research if you care enough, I have no idea how accurate my examples are).
Until you plan on adding any more significant loads, I wouldn't worry much about it. In a handful of years, it may be time to upgrade the panel anyway for your electric car, solar panels, or hovercar.

We may add some loads (new microwave +1.42A, new water heater +4.17A, better AV system +?A) but other changes might offset. I think the key decision will be whether to go with a gas or electric range. These condos had gas ranges originally but some owners converted to electric range later. Our unit still has the original gas line there, so a gas range would be easy. Not sure we want one, but if building code requires that the electrical service pass a load calculation, going with a gas range may be the cheapest way to meet that requirement.