Question

Does the chance for Critical Hits increase with Dire Hit and Focus Energy?

Answer 1

Yes.

According to here, Dire Hit increases your critical chance by 1 stage, and Focus Energy increases it by 2 stages. Since this is +3, your Pokemon will always critically hit (Gen 6) or have a 33.3% chance of critically hitting (Gen 2-5)

Source: Above Link

Comments

It literally says that this combination does NOT stack.

Answer 2

Yes, but only from one source. They do not stack. Dire hit is just an alternate Focus Energy.