Answer 1

Umbreon, being a dark type, can easily fall to Heracross, who is strong against Umbreon with both of its types. Even with a type disadvantage, Umbreon can still take a super effective hit, even from such brutes as Lucario and Infernape. So hit it hard with everything you've got in terms of fighting and bug moves, or use its own strategy against it. Most people use Umbreon just to Baton pass the move mean look, so taunt can mess it up badly. Inflicting status is an option if you're ready for a taste of your own medicine due to Umbreon's Synchronize ability.

Answer 2

Fighting, Bug, and Poison-types all wall and counter Umbreon very well.

Megahorn from Heracross 2HKO's Most Umbreon. (After a Curse, it's a 3HKO)

Close Combat from Lucario 2HKO's. (After a Curse, it's a 3HKO)

Bulky Poisons like Muk can Poison Umbreon, block its Toxic AND Synchronize, and get out-stalled, or force a Baton Pass or switch.