Doom base/Cold Sorc advice

I'm using a Bliz sorc on ladder and have stuff for Doom.

Is there any reasonable reason not to do it in a

Double Axe? And there are no one handed hammers that get 5 sockets, right?

Double Axe kinda ugly to me.

I'm on console and Blizzard is ok, but I'm sort of wanting to use Orb for a bit.

Ice Bolt is the synergy, but I'm curious as to the icebolts that shoot out of the orb. Do boosting Ice

Bolts synergies buff the individual

Bolts?

As for Ice Sorc, does it get better with Infinity and some skillers? Like I have NightWing+ -res Sunder with a protextor jewel, occy and tals atm for the MF and it feels ok but I don't know how much much room I have to improve kill speed wise on P3. I haven't done a respec yet since I haven't found stuff for Enigma/Chains so my Cold Master is nearly 20 and everything else Blizzard wise is maxed.

I feel I'm lagging behind my

Blood Boil friend quite a bit and am trying to find a way to increase my kill speed.

You can do Doom in a

Military Pick .

Not much of a cold sorc player so you'll need to wait for someone else to answer the other questions.