Hello! Both good and bad (but mostly good) news.
Replacing the op-amp has fixed all modes except Vac and mA/A(ac)/ (which I will talk about in one sec). The measurements aren't that far off from my other DMM, however the 87V should probably get calibrated anyway to be able to show its potential; It' supposed to be accurate after all.
That is in fact great! Since, well, the DMM is working almost perfectly fine. Almost being the key word - unfortunately there's something weird going on with Vac and A/mA(ac) measurement functions.
Firstly - Vac - it seems to be okay when in the 600mV range (the auto default when probes aren't touching anything, tho unfortunately I do not have a way to test the measurements in this range) however when taking a measurement of a voltage in any other range, the overload condition occurs. Example - 7V, 32V and 230V AC all return overload. This happens regardless of the range being selected manually or by the auto-range function.
One anomaly is when measuring 18Vac - for some reason it returns 5Vac. I'm 100% sure I am in fact probing a 18Vac source, and that it doesn't drop to 5V when being measured. I have double-checked it with my other DMM.
Secondly - also related to AC - the current measurements.
the DC current measurements seem to be working fine and the measured values are reasonably close to the theoretical (calculated) ones. AC, however, always returns something close to 2-3mA, despite definitely way more (should be ~86mA, as calculated prior to testing) flowing through (judging by the resistor heating up alone).
Not sure if this is one issue or two separate ones which coincidentally both have something to do with AC. Nothing seems wrong with the input sections at the first look, but I'll be taking a closer look just in case. Not sure what to check besides that, what are your thoughts?
EDIT: Oh! And I forgot to mention: replacing the op-amp somehow fixed the battery issue. The wire is no longer required.