[20AccordEXL11]

I wouldn't use a cover if there's the possibility of rain. Water under the cover won't dry, and well, we all know what that can lead to.
Is this parking going to be in a high traffic area where people will notice if someone is messing with it?
I park my car for weeks at a time and have installed a battery cutoff switch to disconnect it. Haven't disconnected it in a while now but I'm driving the car more often too. I have to get my bike down to the beach somehow, right?
I think you're over thinking this a bit. As long as you don't have anything plugged into your AUX connection which might drain the battery more than normal you should be fine IMO. I had an old iPod plugged into mine and I think that's what killed my battery when I didn't drive the car for way too long. I've since unplugged it.

 

[20AccordEXL11]

Here's the one I put on my car. Got it from Amazon so I didn't have to leave home to get it.
If you're having to jump your car any time at all you have a problem that needs to be addressed. Either the battery has a problem or the charging system does. Under normal use you shouldn't have to be using a jump starter at all. Get the battery checked out with a full load testing. I think Wally world and AutoZone will do that for you. Pep Boys too if you have one near you. If the battery checks out as being good, ie holds a charge and no dead cells, then the charging system should be looked at. Remember, a car alternator isn't supposed to be able to bring a dead battery back up to full charge no matter how much driving you do. It isn't designed for that kind of duty cycle, it'll burn itself up.