a = (1,-1)
b = (-2,m)
For two vectors to be collinear, one should be a scalar multiple of the other, that is, a = kb, where k is some scalar.
So, a = kb => i - j = k(-2i + m)
comparing coefficients of i on both sides, 1 = -2k or k = -1/2. Now compare coefficients of j on both sides:
-1 = km but k = -1/2, so m = 2.
For the second question, if two vectors are parallel, then their DR's are proportional. For example,
if ai + bj + ck and di + gj + hk are to be parallel, then a/d = b/g = c/h.
Use this and solve on your own.