Well, to check if it's inserted correctly, check your CP after you insert it. You should be able to feel your cervix through the plastic lining and that the rim is surrounding it. You should be pushing it up there pretty high. I actually had one turn inside out on my while trying to insert it and OUCH!!!
I noticed mine leaked more when I used the bathroom, but wasn't actually planning to change it. Like if you bear down at all, it pushes it out of place and it leaks.
I do remember it being messy to remove and because of the way you have to do it, I'm not surprised it all spills out. That doesn't necessarily mean it wasn't in right. Removing it takes some practice.
What I like about my lunette is that it stays in tact when you remove it, so after some practice, nothing spills out. I decided to use it after BDing the other morning, because I had to get up right away. I wore it a bit lower for a few minutes and after walking around everything kind of dripped into it, then I pushed it all the way up around my cervix. When I took it out, there was proof it was all in there, still was. So we'll see if that worked. We had also BD'd the previous two days though, so if I get a BFP I can't say with certainty the lunette cup had anything to do with it.