Let me help uncomplicate this process for you.
First of all let's make sure it can even be recycled in the first place. Glass & paper are very straight forward. It's the plastic, caps and wands that I'm here to give you the scoop on this.
Have you throughly cleaned the inside? This is a must just like you would with the empty containers you recycle at home.
The colour of the container matters - most recycling plants can't read black plastic. This is a HUGE problem with food take out containers. Maybe this is a silly thought but could they not just program the machine to read black? I honestly couldn't care if my food comes in a black container. I just want to eat it. (my little off topic rant)
Plastic caps are too small on their own to be recycled, but if they’re left on the container they came with, you can put them in your bin. As for pumps, check to see if they have a metal ring in them. If so that would be a mixed material so you wouldn’t want to have that together. Take the pump off, put that part in the trash, and then put your empty package in the recycling.
Mascara wands - I found a super great program called Wands for Life that I love. Old mascara wands are used to remove fly eggs and larva from the fur and feathers of wild animals. They work great because the bristles are close together. How awesome is that?
As for lip applicators they have to be thrown out unfortunately. The positive thing is that packaging options are changing and my goal is to be 100% fully recyclable in the year to come. New advances in sustainability are happening and what an exciting time for important products like this to finally come into being.
The future is bright my friend!