Connect a normal 12 Volt 150AH C10 battery with a solar 12 volt 150AH C20 battery in series for the 24Volt solar system

Based on my experience being qualified as a battery charging electrician on submarines and installing/upgrading/maintaining the 12v electrical system in my motorhome.

1. Battery electrolyte specific gravity is not model or battery specific so your chart is fine.

2. Amp-hours is a measurement of current consumed (or the sheer number of electrons you've pulled out of the battery) rather than tracking watts which is a measure of power. You can easily track the amount of power used, but it would be impossible to determine the actual state of charge in your battery. It would be like if you tried to gauge how much fuel you had left in your car by reading a "cumulative horsepower meter".

3. A manual hydrometer is fine - just avoid the super cheap ones available at the auto parts store.

4. Get a real battery charge monitor that measures amp-hours in/out. I use one made by Xantrex.

5. You have to test the battery to know its bad.

6. An equalizing charge involves holding charge current at a low value, which boosts charge voltage - so if your charge controller won't allow you to set EQ current at a value, get a new one. 10 amps is probably close enough to the charge rate appropriate for equalizing - however if your array is only capable of delivering 10 amps with full sun, you might want to reconsider that strategy.

7. Who cares. Battery capacity is a function of the rate of discharge so that value is effectively worthless to you as a monitoring metric.

Since you have an old car battery, the cost of damaging it by overcharging isn't much ($40?) and that would only happen if it got a lot of sun over weeks. A small home solar system might have thousands of dollars of batteries, so standard practice has long been for those to always have charge controllers.

For small systems the cost of a charge controller used to be significant so it was common to forego it in favor of simplicity. However, there are now very - inexpensive - controllers which no longer as easily justify the old practice.

If you can afford an additional $25, you might as well do it right. Also, it would come with instructions on what to do.