For dripping I use an empty cart as a mouthpiece, and just drip 2 drops into my 510's atty at a time. While I can get away with 3 at times (if its dry or the juice is thick etc) I find that risking a leak is more trouble to clean up than dripping 2 drops at a time more often.
Something to keep in mind tho, not all drops from all bottles are the same size, so if you find 4 drops leaks, try 3, if 3 leaks sometimes, either risk it for more vapes between drips or just use 2

(posted this for those that use 4 or more drops, the type of atty also affects this, some can take 6+ but not mine)
My atty's only have 2 air holes here, I expect you have a REALLY light drag with the 4 hole type there. As your stock carts seem to be leaking when you refill them, I would suggest getting some stuff to replace that with. If the filler is not tight enough it will leak just from gravity (thinner juices will be most prone to this)
As filling a cart with fluval or polyfill or the tea bag matierial or the blue fish tank filter pads is not an exact science it will require some trial and error to get the right ammount of filler in, while still letting enough fluid wick into the atty to get a good vape. And as I mentioned the thickness/thiness of your juice will affect this also. (Also some stock carts will have less filler than others and be more prone to leaks, not an exact science to be sure!)
I would suggest experimenting with plain PG (THIN juice) and or VG (THICK juice) and different filler types/ammounts to find what works out best for you. This way you wont waste expensive juice while finding the right ammount / type of filler that works best for whatever your vaping.
The best stress test I found is to fill a cart, pop it on the atty and draw on it as hard as you can a few times as that is most often when one will leak for me if the filler is not tightly packed enough in the cart, or is too pourous etc.
As far as the atty itself goes, when you look into it you see the raised bridge, that part is intended to make contact with the filler in a cart and wick juice from the cart, past the bridge and deeper into the atty where it is then heated to make the vapor.
Hope this clears that bit up for you
