As it is shown by Hawking the area of the events horizon never decreases,
but it depends only on the mass of the black hole and it's rotation speed.
But when the hole evaporates it's mass decreases until in won't become a Plank's black hole. What happens to it's events horizon while such evaporation?
Does it's rotation speed increase so it becomes more and more flat ellipsoid looking like a pancake with same area?

The evaporation is a quantum process, but the Hawking's explanation with two light rays going on the events horizon is unlikely to be violated even in quantum mechanics.

Actually Hawkings radiation slowly decreases the mass of the BH. This only occurs when the surrounding temperature is less than the blackbody temperature of the BH. As the mass decreases so does the event horizon. As the event horizon is determined through the Shwartzchild metric which involves the mass.

 

As far as rotation goes this is a complex question.One would expect that conservation of angular momentum would apply and it does so the angular momentum should increase as the BH shrinks. However there is also Berkenstien radiation. This and other forms of particle production and quantum tunnelling is theorized to reduce the angular momentum.

http://arxiv.org/abs/1104.5499

 

This article covers what I just stated however it's extremely lengthy and technical it does a great job covering BHs in particular the accretion disk processes

As mass of the BH decreases due to HR, so does proportionally the area of the horizon.

The area of a spherical object will decrease faster than its radius.

I would think a BH's angular momentum would decrease.

 

This of course depends on the specifics of the moment of inertia of a BH, which I'm not too familiar with.