Electrical – Meter and service panel separate from house

Your real problem is a lost neutral.

That's why your voltages were going all 80-240V. The neutral wire broke between the panel and the pole. This needs to be fixed. Unless it's in your panel, it's the power company's problem and should be reported as a power outage, which it actually is. Shut off everything until it is.

If hooking up a ground significantly improves conditions, that diagnostically proves the neutral problem, but This is NOT a legitimate or safe fix!!! It should not be continued for even one more minute. Shut Everything Off and get that neutral fixed.

Since your panel does not appear to have a main breaker, you would need to call your power company and have them come out and pull the meter. They need to do that anyway to investigate the lost neutral.

Now might be a good time to get a meter pan which contains a main breaker. I would obtain it and have it ready for when the power company comes out to fix the neutral. They may just fit it for free, since they're in there anyway, and replacing beats troubleshooting.

Other stuff

The nice thing about a main breaker on the meter pan is if you turn it off, your entire panel is deenergized, which makes the panel safer to work in, and makes a whole-panel replacement safe to DIY. Not that there's anything wrong with a QO panel! It is small for my tastes.

However I think you definitely do have a split-bus "rule of six" panel.

Fill the empty hole in slot 28 with a spare breaker. They make proper blanking plates, but I find them flimsy and expensive, and breakers are cheap and a heck of a lot easier to find. Label it N/C.

The zinc plated copper ground wire is fine. You can't use aluminum for ground wires.

The big aluminum is fine and in fact preferable, since the lugs are aluminum. Beware of small gauge (12-8 gauge) aluminum wire in the house on branch circuits. That is the scary stuff. Until recently, the repair approach was to run around screaming and tear your hair out, then tear your wire out. Today, there's a magic device called an AFCI breaker which will catch arc faults, which is what we're worried about with aluminum wire. That, with CO-ALR terminations or Alumiconns, I'd sleep well at night.

It's definitely a Rule-of-Six "split bus" panel.

Now, the dead giveaway of a Rule-of-Six panel, look at the top 12 spaces (where the six Rule-of-Six 2-pole breakers go). Follow all their wires. Are they all accounted for? NO. Breaker 1's extra fat wires do not leave the panel.

Its top wire does a most unlikely thing, that seems like an optical illusion but is not: it goes straight down, just to the left of the L1 lug. Look close in empty position 9, you can see it again just left of the bus, with that same spackle splattered on it. And just to the right of the L2 lug is an equally fat wire that is mostly obscured, that can only be its partner. Split-bus panel.

Now look at Space 14, right side. Compare to spaces 28 and 30. See how the bus is different there, as in weirdly missing? Split-bus.

I'm not a fan. I would transform any Rule-of-Six panel into a Rule-of-One panel by having only one breaker in the Rule of Six area. QO makes snap-on breakers as large as 200A that will fit there, then I'd feed an external subpanel. (the internal subpanel is too small).

** If you really know what you're doing, you can activate certain loads, e.g. 240V-only loads (which have no neutral).

How to handle this

I'm going to presume that there's a panel here (if not, I'd slap a decent-sized main breaker loadcenter in there, a Siemens P3030B1100CU would be my starting point, and then add the appropriate breaker for the well pump and hook it up), and that we don't have to worry about the generator itself -- it has overcurrent protection in the form of a circuit breaker built in.

As a result, we can simply pull the bonding screw on the loadcenter/panel, and then wire a generator inlet box (locking type, 50A, 120/240V) to it using a 6/3 UF cable such that the hots land on each hot leg of the main breaker, the neutral lands on the main neutral lug, and the ground lands on the main ground lug -- if the panel has no ground bar in it, you will need to add one. The inlet box will mount to the outside of the shed, by the way (this saves the generator cord from having to be run through a door or window frame).

Once you're done with that, you can then run 6AWG copper from the panel to two driven ground rods, spaced 6' apart, as well as a length of 6AWG copper from the panel to the well casing if the well uses a metal casing. This takes care of the grounding electrode system.

Once all this is done, you simply take a 50A generator cord, plug it into the generator power receptacle and the inlet, and all should work. Since things are in a separately derived system configuration, you don't have to fuss with the bonding jumper in your generator at all, and if you want to replace the generator inlet with a permanent feeder in the future, the panel's already configured for that.