What’s the usage of storing recorded measurements of multimeter and soldering iron station in computer

100mA pulsed at 50% duty cycle for 16 hours equates to 800mAh. If your battery had much larger than 800mAh capacity then its voltage might not drop much, and might even increase if its temperature rose or it had previously been under heavy discharge. However if you keep the circuit running for long enough the battery voltage should start dropping.

The 'ground' in your circuit is just a reference point. The only path the current can take is from battery +ve to battery -ve. Current in the wire between the load and 'ground' is flowing towards 'ground', and current in the wire from 'ground' to battery -ve is flowing away from 'ground', but no current can flow into or out of the 'ground pin' itself because there is nowhere for it to go. At all points in the circuit you should measure the same current flowing and always from battery +ve to -ve (eg. when measuring current in the wire between 'ground' and battery -ve, the meter's positive lead would be connected to 'ground').

Your diagram perfectly illustrates what the current should be doing. However it does not show the complete circuit with all components (load switcher, ADC etc.). Are you sure that this extra circuitry is not somehow feeding current into the battery? If you find that battery voltage continues to rise rather than drop then you will have to analyze the entire circuit to find out why.

I rarely use the feature but for more precise measurements it can be useful. For example if measuring a sensor I might want to make a note that the meter reads 2.984 V and it's more convenient than trying to remember the value while I write it down on a piece of paper or enter the value into a spreadsheet etc.

Sometimes too I might be in a position where it's hard to read the meter output at the same time and I can rest my little finger on the hold while positioning the probes.

Some higher end meters also have an auto-hold type feature where once the reading becomes stable they will take the measurement and hold the display. That's a feature that I find much more useful because you don't have to keep your eye on the meter at all and they will beep when the measurement is done.