If you are driving your car in the positive direction and hit the brakes, your change in velocity will be negative, so your rate of velocity change with respect to clock time, which is the acceleration, will be negative.

If you were driving in the negative direction and hit your brakes, then your acceleration would again be in the direction opposite your velocity and would therefore be positive.

In .5 m v^2, v is the speed and not the velocity. The velocity vector has speed and direction, and you're not squaring the direction, only the speed.

If we're moving along a line where velocity can be positive or negative, sometimes we actually write the - for a negative velocity and do something like .5 m ( -3 m/s)^2. Strictly speaking we shouldn't include the - sign, but it's going to square out anyway so it does no harm to include it, and including it helps us relate the calculation to the rest of the problem.