Welcome to the group. Your best bet is to get a schematic/service manual from the manufacturer.
Here are some educated guesses- you're likely right about the pots that you've found. Watch for interactions between the adjustments- sometimes they aren't completely independent. This is where a test procedure/service manual could help.
On the -.7v, when off, this is likely the charge on the output cap clamped by a reverse polarity diode on that little board on the front panel. Load it with a 1k R and see if goes away consistent with value of that Cap - T=RC. A better instrument might have a 10k R across the C to deplete this- in your case, it gets down to .7 and has nowhere to go once the diode stops conducting at .7v.a
My guess for the mystery pots is switchover points that tap the transformer secondary at different voltages. This is common in high current variable linear supplies. At lower output voltages, a lower voltage tap is used to lower the voltage that the pass transistor has to take. If you wanted to make 1v at 5 amp from a 30 volt, basic transformer and rectifier, the pass element would have to dissipate nearly 150W. If you use and 8v tap for these lower voltages, you can limit this case to 35W, much more manageable. Its likely there are three secondaries, a high voltage one- say 30V, a medium one, say 22v and a low around 8V. The output pass element has to dissipate the drop in voltage times the output current.
Get a schematic somehow and have fun. I've told vendors that due to being an ISO 9000 shop, all our equipment had to be fully documented. They coughed up schematic from somewhere. Good luck.
Good luck.