Android doesn't like when a device shuts down due to low power (0%), as evidenced by many threads about people losing data, or corrupting something and can't boot up, due to doing the exact thing you seem to be doing. Like H3aTeRzz stated, don't let it drop too low. Personally, I charge when the battery reads somewhere around 35%, and rarely lower. It could be your battery is just getting old, or has developed a dead cell or something... not sure exactly what's going on, so that's just a guess. As a reference, my 10.1 2014 can get over an hour of use and sometimes going as much as an hour and twenty minutes per 10% battery drain depending on my use. Even if I heavily use it, I'll get over 8 hours. If your tablet isn't getting these times, then I would guess your battery is simply aging and might need replacement.
As far as using the Insigna charger, the tablet determines what power it needs from the charger. It doesn't work the other way around where using a more capable charger will charge things faster. The Note 10.1 2014 doesn't have quick charge circuitry, so no matter which charger you use, the tablet sets the requirement, not the charger. The fact that it might seem it's charging quicker with the Insigna might mean your other charger can't seem to supply the needed power or it just got tired, or if it's not the charger that came with the tablet, it's underrated. I would tend to lean more to the fact that you're allowing your tablet's battery to fully discharge rather than it being the Insigna charger causing issues.