I haven't read this whole thread, basically the first page, and last two pages. But I just want to say congrats!!! on getting off the stinkies!
If I'm visualizing this right, the "white stick" is something that you'll find in every carto cap (sometimes called a condom). I think it's in the larger one, and you probably haven't seen it yet because no others have fallen out. But check the caps of others and see if your white stick is them too.
I'm really new to this as well. On my first order, I got my Riva kit (kgo clone) and yes the kgo is a 510 connection. The kit I got came with 5 mega dual coil filler cartos, and I bought the 15 pk of boge cartos, plus 5 more mega dual coil cartos. Got my juice, started vaping......and very quickly realized that filler cartos are NOT for me. The first couple days were fine, then every hit was dry, scratchy, just awful, even though there was plenty of juice, and they were not burned. Took one apart to make sure. So, at this point I figured I needed to try clearos. Of course everyone had their own ideas of which ones were best. The thing that helped me most.......was going and watching videos. So if you haven't done that yet, I'd really recommend it. You'll see the ones that love a particular thing, and the ones that don't love it, and more importantly, what their issues were with it. What might be an issue to some, may not be a big deal to you. But just having the visual of the videos, seeing the actual items and how they worked was a huge help to me in deciding what I wanted to try first.