No problem having 10% as "constant current". The important factor here is how much intensity variation your eyes will be able to see without having a better reference point to compare with. Our eyes are truly lousy to estimate absolute light intensity.

The quality of "constant current" is just a question of needs. In some applications, 0.01% variation is too much. When driving a single LED, 10% is very good. Remember that this is not an application where you have thousands of LEDs close together, allowing your eyes to compare them.

You really do have to recognize that different application areas have different needs. Do not ever consider a LED display panel as a good reference when comparing with indicator style instrument-panel use. And your constant-current drivers may work well in your LED panels but are truly lousy for generating a constant current in a precision instrument.

Yes, 10V is an almost dead lead-acid battery. You should normally cut the load even earlier - say 10.5V - since the depth of the discharge greatly affects the number of cycles the battery can stand. And at 10 or 10.5V, you don't have much energy left in the battery. You really have to separate "fully discharged" for a rechargeable battery and for a primary battery. A Li-Ion battery is considered fully discharged at about 3V - there is still energy in the cell, but a deeper discharge means it may catch fire when you try to recharge it.

In the article, the battery technology is not mentioned, so we don't know if it is capable of a higher voltage than the nominal 12V. While a Lead-acid battery can have 15V charge voltage, the voltage will quickly drop to around 13.5V after the charging current is removed. But if discussing 10 1.2V NiMH or NiCd cells, the usable voltage range will be very small - in the region of the claimed 10%.