I need the explanation on a DMM instruction manual
I would interpret the Regulated Power Supply specification to mean that the DMM is guaranteed to work with a battery voltage of 2.4 + .15 or 2.55 volts and maybe down to 2.4 - .15 or 2.25 volts. In any case, operation is not guaranteed if the BAT indicator lights up. Thus, to answer your question, it might work with a voltage of 2.4 but it is not guaranteed. The Accuracy warranty period of 1 year simply means that the DMM is guaranteed to meet its accuracy specifications for a period of 1 year (presumably starting from when it was manufactured).  AFter that, the manufacturer will not guarantee that the effects of component drifts have not caused the DMM to fail one or more accuracy specifications.  It does not mean that something happens after exactly 1 year.  This is a perfectly normal specification for most electronic measuring devices. The time period might vary depending on the initial accuracy specifications and the quality of the components.