Just so you know, you can give it the colorless frame by setting color from "Auto" to "colorless."

Also, if it has shade in the name it really ought to have the creature type. As it is, it isn't Kozilek's Shade so much as Kozilek's "thing that does shade stuff but isn't actually a Shade," which already exists (Sludge Crawler). Speaking of which... Why is this white? The only instance I can recall of white getting this sort of pump is Shade of Trokair, which was from Planar Chaos.

White's supposed to get toughness pumping almost exclusively. Colorless seems to get you asymmetrical pumping, but the combination would probably be best with +1/+2 for slightly more.

A bear that has wither; AND pumps +1/+1 for ? Yowsers. Ok, it can't deal damage to players; so it's basically purely a blocker (and wow does your set have a lot of those) unless you're doing a mill strategy; but still. Powerful much?

The set does indeed have a lot of those, which does indeed enable a mill strategy. The voidwarp creatures are stronger vs other creatures but weaker vs players.

Note that this is very different to "pumps for ". is fairly hard to produce unless you're in a dedicated deck. It does look a bit odd to see this in white rather than black, though.

The name was supposed to be playt-ishand describe what the cards do, and not be an actual shade (Eldrazi names are hard to come up with). White and Black are the two colours that are allowed to get single mana +1/+1 pumping until end of turn. See Blessing. White is also allowed to pump for power for rare occasions Capashen Knight, Duergar Cave-Guard and White Shield Crusader. While white is tertiary in these effects, in is allowed to get them. The point of the Eldrazi is create card that feel odd which is why this card is white rather than black. (This why Swarm Surge gives first strike, why most red eldrazi have toughness that power.

I am considering to change the card to [1][C]; +2/+1 until end of turn, although that competes with Havoc Sower. +1/+2 compete with Stalking Drone and +1/+0 competes with Kozilek's Shrieker. I should make a [C]: +0/+1 variant but I don't want to put in in white, as that the colour this effect would normally be. (possible blue or black)

I think white getting +2/+1 (for ) would be in-pie but unusual, which fits what you're after here.

Alternatively you could go for something odder, like : +3/+0.

The +3/+0 is a delightfully weird idea and does have a precedent in Restless Apparition. I might do that and shift the "C: +1/+1 until end of turn" into Green which also has access to the shade ability Ursapine.