Home Brew Ohio M6-UB3E-15H1 Portugese Double Lever Corker

My corks do not go all the way in and have a "hump" on one side. How do I fix this?

Can I use this with a #5 tapered cork for a very small bottle? The cork is 17.mm across the top.

What size cork works best with this corker?

Will this work for champagne bottle corks?