Let me try to answer question #2:
Set each part of f(x) = x for the domain of that part.
1) 2x + 1 = x for 1 <= x <= 2
x + 1 = 0
x = -1 Since this value is not within 1 <= x <= 2, there is no answer for this section.
2) 7 - x = x for 2 < x <= 3
7 = 2x
x = 3.5 Since this value is not within 2 < x <= 3, there is no answer for this section.
3) 10 - 2x = x for 3 < x <= 4
10 = 3x
x = 3 1/3 This is within the domain, so this is part of the answer.
4) 10 - x = x for 4 < x <= 5
10 = 2x
x = 5 This is within the domain, so this is part of the answer.
Answer: 3 1/3, 5