Barto's barrier is invisible and most likely made up of air. Inazuma has only cut solid objects and not water or air, so for now I doubt the Snip Snip can do anything. Same can be said for Senor Pink and Morley's Devil Fruit against barriers.
Both would take place IMO. Pica's rock becomes wavy but he's still able to move around inside and manipulate the shape. If Pica wants to stop the rock from waving around, that's a power clash with Diamante and the one with higher mastery wins.
Again, it's a power struggle. It's not different than Akainu's Magma Fist vs Whitebeard quake punch clashing.
All three. Natural relationship like Rubber vs Electricity, who has higher mastery over their power, and Devil Fruit hierarchy like Magu Magu > Mera Mera and Hie Hie > Yuki Yuki.
Some interesting natural counters I would like to see tested include:
Hancock vs Pica
Kizaru vs Blackbeard (Yami Yami) and Moria
Law vs Buggy
Apoo vs Corazon
Kizaru vs Shiryu
Betty vs Perona