I have this battery charger at home. It has a voltage test function. I also have a lot of non-rechargeable batteries lying around. Is it possible and safe to use the charger's test function on non-rechargeable AAA or AA batteries?
That charger device clearly states that it is for NiCd and NiMH rechargeable batteries only. It would be a risky proposition to put other batteries in that unit whether they be lithium or alkaline types. I think it would be just too easy to put the unit into the wrong mode.
What you want to do instead is get yourself a digital multimeter that can measure voltage of any battery that you may have laying around. These days you can pickup a suitable device that would fulfill your needs for a surprising low cost. Check out offerings on Amazon for example. The good thing about this approach is that you will find other uses for a digital multimeter once you have it and learn how to use it.
I have a suspiciously similar LaCrosse charger that I have used for testing alkaline batteries. My charger spends a few seconds detecting and displaying the voltage before it begins charging, so if you're a bit quick, yes, you can use it to test voltage.
No. It is made for NiCd and NiMH batteries only, which happen to work at the same voltage. The charge indicator will be useless for any other type of battery, which by nature operate on different voltage.
Buy a real DVM, measure the actual voltage, and google up a table that shows voltage vs. state of charge for that battery type.