If these were posted separately, as in one question per thread, I could help you more.

Since you only need hints, maybe no use to separate them anyway. (But it will be better if you post questions one each per thread.)

1) The tangent line along the y-axis is perpendicular to a radius of the circle. So the center of the circle has a y-coordinate of 2.

2) Do it by the popular method: get dy/dx, etc.

Or, if you're not into Calculus yet, the slope of the tangent line is the trig function tangent value of the angle made by the tangent line with the x-axis.

See if you can find, using this way, that m = -3/2 for the said tangent line.

3) A standard form of the equation of a circle whose center is at (a,b) and whore radius is r, is

(x-a)^2 +(y-b)^2 = r^2

You have 3 given points on the circle, ... you have 3 unknowns, ... so?

(Substitutions)