I received my first reomizer the other day (have another on order). The stock wick that comes with the reomizer does not touch the bottom. It just sits, floating, in air hanging from the two posts. You do not want to push it down. You don't want any part of the coil touching either the side or the bottom of the reomizer body.
Think of it like the heating element in a hair dryer. As others have said, pull off the drip tip, squonk and watch for liquid to make contact with the wick. Now that you've got the o-ring leak issue resolved I think you will see it behave differently than it did before.
Make sure you keep the coil separated from the metal parts of the reomizer, other than the ends that pass through the two mounting posts.
The supplied wick is very short but works well. Squonk, watch the liquid make contact with the wick/coil, wait a few seconds, take a hit or two. When it begins to have a little burned taste (maybe 4-5 hits), squonk it again. Practice makes perfect and it'll become second-nature.
It sounds like you might be new to the whole e-cig thing. Vaping can seem very harsh to the throat when starting out. If so, try going through the whole inhale/exhale process without opening your mouth - use your nose. That dulls the harshness, and increases flavor IMO. You just have to try it to see what I'm talking about.
This will make sense when you get to the point of making your own coil/wick. Or when you order some pre-built ones from
somewhere. Tinkering with this small electrical stuff takes some knowledge and experience. It'll come to ya.