Lower current is better than higher, as it will keep the internal heat of the battery down. Remember that a flat battery is like a super capacitor. Like a glutton, it will suck up whatever is available. Feed it little bits at a time. Voltage needs to be exact, amperage can be recommended level OR LOWER.
This is because current is decreased with higher resistance. Current equals voltage divided by resistance (i=v/r). So the higher the internal resistance, the lower the current output ability. Low internal resistance batteries are much better at supplying high current pulses.
So twice the power for half the time is the same amount of energy drained from your battery. EDIT: If the question is why would the battery capacity decrease over the expected ideal, then Brian's comment is the answer. The internal battery impedance means more power dissipation at higher currents.
Depends on the battery chemistry. For lithium ion, it's usually not a problem and can even be a benefit. For NiMH, a charging current that is too low can make it dificult for the charger to detect the point where the battery is full, which can lead to overcharging and overheating the battery.
The electrodes and electrolytes aren't 100% conductive. So they will have some resistance (internal resistance) in them. Ideally, a battery should have 0Ω internal resistance. So during battery operation, all the voltage will be dropped across the element that the battery is powering instead of the battery dropping voltage across itself.
Efectively extending battery life in future devices will require mastery of low quiescent current. This paper examines the role of low quiescent current in delivering the battery life essential for today’s (and tomorrow’s) wearable, mobile, and other smart, connected devices.