Q1 looks good except for x = 2 you had y = 4/3 instead of -4/3.
Also you did not find point of inflexion, only x value. (y value will be -2/3)
Q2 - basically - you need to show it touches the curve once.
x - 4 = x2 - 5x + 5
x2 - 6x + 9 = 0
b2 - 4ac
= 36 - 36
= 0
so one solution.
As there is one point where the line touches the curve it is a tangent