Joe, you were wondering why they used 2 sets of batteries for the resistance ranges. The simple reason is that the 9V battery is not ( at least in the regular zinc carbon variety) able to supply 100mA or more, which is needed in the lower resistance ranges to drive the meter to full scale. Using a single ( in your one 2 AA cells so you have enough voltage to drive the LED and the buzzer, otherwise the regular version uses a single cell only) AA dell will make it able to supply the required current for a long while ( at least long enough to measure 100 or so seconds at a time) without the terminal voltage dropping due to the cell internal resistance rising as it polarises internally with the reaction products. A 9V battery will polarise very fast at 100mA ,in the order of a second or so, but at 1mA or less it will take a long time.
Resistance readings you need to set the zero every time you change range, and do it again after every 100 or so readings as the batteries age and change terminal voltage. However these meters and others of the same type were very common in repair shops decades ago, and served very well to fix almost all equipment that came in. They however are not so useful now, just from the loading the constant current draw ( the ranges DC and AC are basically designed to draw a similar current at FS on each range, so they are pretty heavy loads on modern equipment) is not something you have to consider with a modern meter with a relatively constant high input impedance.
As to the AC range, those meters almost invariable are calibrated to read an average voltage with half wave rectified AC, but are calibrated so the scale reads RMS voltage instead. Thus on AC with DC applied they read high by around 30%, but for the use of checking transformer AC voltages this is fine. As well the AC voltage ranges are non linear at the bottom end, simply because they tend in modern meters to use a silicon diode, as opposed to the original use of a germanium point contact diode, with it's lower forward voltage drop. Basically AC voltage below 20% of full scale will be inaccurate, but that was often pointed out in the older manuals.
As to those extra diodes you added, very nice, I should add them to my old Hioki meter, as I have burnt a few resistors, funny enough pretty much those you cooked
in the years I have had it. Was new in around 1980 when I got it as a birthday present. Still use it as well.
You were wondering how they damp the meter movement from damaging itself, which is done using the aluminium former that the movement coil is wound on. This forms a shorted loop in the meter magnetic field, and thus provides a frictionless damping for the meter needle, damping fast acceleration by being both an eddy current damper in the magnetic field of the magnet to fast angular acceleration of the needle, and also being a shorted turn in the transformer formed from the coil and conductive frame so reducing the effect AC current has on the meter movement. However the pivot mountings are the weak point, dropping the meter often either breaks the pivot off of the coil as the drop of shellac holding the pin there breaks, or it bends the pin and adds a massive friction load with the bent pin, or simply moves the coil into contact with the frame, or out of the linear portion of the gap field making the response less linear than it was.