You're right, the wick slowly drips the juice onto the atty. You can take the the spike out, but hang onto it if you want to use it in the future. Be careful not to pull the wick out, though, because it's a ..... getting it back in. Lots of people, myself include, drip straight into the atty (onto the coil) without the spike. Drip about 2-3 drops at a time, and redrip as the flavor starts to turn. You may want to get a drip tip, though, because the metal on the atty will get quite hot and slowly chafe your lips (I found that out the hard way). I believe the burnt smell/taste comes from the coil burning the wick because there isn't any juice feeding to it from the tank, but now that the spike is out, you'll get that burning taste after extended use without cleaning the atty. My method for cleaning is to blow it into a tissue until no more juice comes out. Then, soak it in rubbing alcohol for about 15-20 minutes (agitate it every now and again). Rinse it out with hot water, and/or boil it on the stove for about 15 minutes. Some people warn against tap water, but I haven't had any problems. Also, some people have said this has killed their atty's, but again, I've never had any problems. Blow it out once you're done and set it to dry. It shouldn't take long. I put mine on the vent of my air purifier for about 10 minutes, blow it out again, then slowly heat it up until I see the coil burn red. As far as the juice leaking into the battery, are you using a manual or automatic? That could happen with an auto, but a manual has a closed system so there are no cavities for juice to leak into.
