Highly unlikely.
No, a bad coil will not drain the battery.
there is a short some where in the electrical system... or a bad battery.
If it stays on all the time it will drain the battery
bad ignition switch, bad battery, bad alternator/regulator,
Your alternator could be bad.
No, it can cause you to use and excesive amount of fuel but it will not effect the battery.
Bad Battery. Bad Alternator. Lights left on by mistake. Something left running. Exc.
Could be a shorted wire, or bad battery.
Bad battery or a parasitic drain
Good possibility
Yes
No.