2 & 3 are true.
Q1) False. A counterexample would be x = -0.5 = 1/2. (0.25 > 1/8)
Q2) True. Given that x is negative then 
Q3) True. I think there are two ways looking at this. x alone is negative and 1/x would be negative making the sum negative.
The second way would be to find a common denominator. The fraction would be 
with the top being positive (for all x) and the bottom being negative (as x is negative). This fraction is neagtive.
Q4) False. A counterexample would be x = -1. Left side is -1 and the right side is 1. It would be true if x is negative and the left side was negative x.
Edit: Fixed typos.