Campy 11 speed and Shimano compatibility
Derailleurs: No. Shimano and Campagnolo derailleurs have different actuation ratios, and while there are adapters for many other combinations, Shimano to Campagnolo 11-speed isn't manufactured. The cassettes are so close that you can use cassette from one 11-speed system with the other, so there's less need to mix derailleur brands.

Mechanical brakes: Yes, but not optimal. Newer Shimano road brakes use slightly more cable movement for the same brake actuation, so Campagnolo levers will work with them but feel spongy and if you don't keep the brakes well adjusted the levers may hit handlebars before maximum braking power.

Hydraulic brakes: From what I could find, both brands use 22mm pistons, 5mm hoses and mineral oil based brake fluid, so they are not fundamentally incompatible. I wouldn't try it myself, since brakes are the one component you don't want to fail.

Edit: Regarding the other answer, the fluid transfer amount is determined only by piston cross section area. Shimano and Campagnolo road brakes apparently have similar sized pistons, but this doesn't apply MTB models, different brands and future models. The fittings are different, but since hose size is same, you should be able to install fitting from different brand on one end. I still wouldn't do this and shifting wouldn't still work.