Question 1)
Dividing every term by 2 will yield you with:
x² - 10x + 25 = 0
This becomes: (x - 5)² = 0
Thus, there's only one solution.
Question 2)
Finding the slope using the two-point slope form will give you a constant of 1. Since along all of the points gives you a constant slope of 1, we know it is a linear line.
So, it looks to me that (A) graph is the correct graph.