I’m not 100% sure those will fit big pulleys for pneumatic wheels, but maybe without the idler? Someone else please chime in
Without knowing if this will be your only build, I highly recommend just buying a battery that will fit whatever enclosure you choose for your build from a skilled battery builder on this forum: [WIKI] Trusted Battery Builders (Serious)
Long story short, new Unities are sold by a scammer / internet douchebag, but the good news is that you can buy a Xenith instead from Build Kit boards, which is basically a clone of the Unity, but with quality control to make sure it’s working, and a warranty of course 
Although with your budget / build, you might want something a bit fancier and powerful, like a Stormcore 60D or dual Torque ESCs. Based on newer hardware, might behave better. YMMV
But do you have an enclosure for it?
And then end up spending months looking for a compatible enclosure? Nah, you gotta order parts / plan your build in the right order:
Someone else can assist you with trucks / wheel choice; I’m not an expert on DKP.