Undispellable Debuffs

Is it possible to create buffs or debuffs that cannot be dispelled? If so, how?

Base them on auras and add/remove the aura from the targets of said buffs.
Slow Aura (Tornado) is a classic choice for this.

Also, some buffs are naturally undispellable.
Doom, for example.

Ok, new random question....

Do ultimate abilities eat through spell damage reduction items?

Nope.
They bypass spell immunity, but they still factor spell damage reduction.