You should be able to use any kind of cuticle remover with any system as long as you remove it well and dehydrate afterwards I usually only use Nail harmony cleanser to remove cuticle remover and haven't had any lifting problems
There should be no excess moisture in the nail plate after washing off the Cuticle Away because you will dehydrate before applying your product. Alternatively you can just do a dry manicure to remove the cuticle.
I don't see why you can't.
If you make sure you do a thorough prep, cleanse nail correctly and then dehydrate nail correctly before application, then in my opinion it can only give positive results because there is no way that a nail can be totally clean of cuticle, dirt, oils and moisture unless you do a thorough prep using a cuticle remover and dehydrator.