To answer the first half: If you don't need to ever use the double-less-than symbol, (and double-greater-than) you can simply redefine them using a show-rule:

#show symbol(math.lt.double): symbol(math.angle.l.double)
#show symbol(math.gt.double): symbol(math.angle.r.double)

However, this will change all instances of math.lt.double, not just the ones you get with <<.

It is possible to only apply this change to math-mode, by doing:

#show math.equation: it =>{
  show symbol(math.lt.double): symbol(math.angle.l.double)
  show symbol(math.gt.double): symbol(math.angle.r.double)
  it
}

I don't know how to achieve the second half, replacing +- with ± in math-mode.