The complex number u is defined by \(u = \frac{6 - 3i}{1 + 2i}\).

1. Showing all your working, find the modulus of u and show that the argument of u is \(-\frac{1}{2}\pi\).
2. For complex numbers z satisfying \(\text{arg}(z - u) = \frac{1}{4}\pi\), find the least possible value of \(|z|\).
3. For complex numbers z satisfying \(|z - (1 + i)u| = 1\), find the greatest possible value of \(|z|\).