Problem 1

First of all, check that the spring on both sides is well adjusted. See "Spring Adjustment" on this page by Sheldon Brown.

If not, it might be slightly more serious, but not terminal. Indeed, that's a problem I have at the end of each winter. Fortunately, the fix is cheap.
– Remove the cable from the arms so it's not under tension.
– Unscrew the pivot bolt (either allen key or wrench).
– Remove the offending arm.
– Clean thoroughly the pivot and the place in the arm where the pivot sits. It's probably full of grit, the grease is dry... I typically use WD-40 to clean both parts and let dry completely.
– Check that the spring isn't broken (unlikely, but it happens, in which case you'll need a new spring).
– Grease the pivot liberally, re-install the arm.
– Do the same with the other arm, because the problem will arise within 2 weeks.


Problem 2 – front wheel problem

At first reflection, it sounds strange, because cable length doesn't change when you turn the wheel. I see a few possible causes:
– Springs way too weak (see "Spring adjustment" above).
– The rear brake or one of the shifter cables interfere with the front cable and moves it sideways; in doing so, it "de-centres" the brake.
– It happens only when you turn the wheel completely, in which case it's simply because the brake arm touches the downtube. Not a real problem in real-life.
– Your front wheel wobbles, has very loose cones, slack spokes, etc. so it's actually the rim that moves sideways when you turn. It's unlikely, but I've seen it.