Which describes a solution that contains a system at equilibrium?

The solution where the color is not changing is at eqiulibrium. If the color is still changing, then the concentrations in the solution are still changing and the system is not at equilibrium. 

2. 
When Br- is added, the reaction occurs in the forward direction to use up some of the excess Br- added (LeChatelier's principle). 
a. 
Cu(H2O)6+2 - decreases 
Br- - increases, because not all the added Br- is consumed 
H2O - increases 
CuBr4-2 - increases 
b.  
K doesn't change unless the temperature changes. 
c. 
The color would change from bluish to greenish because te Cu(H2O)2+ (blue) is decreasing and the CuBr4(2-) (green) is increasing. 
d. 
The tube would feel cooler because the forward reaction occurs to use up some of the added Br-. Heat is removed from the surroundings when the forward reaction occurs, so the tube feels cooler. 
3. 
Mg(OH)2(s) <==> Mg+2 + 2 OH- To make this reaction proceed to the right, you need to remove either Mg2+ or OH-. One way of removing OH- is to add an acid. The molecular equation is: Mg(OH)2 + 2HCl ---> MgCl2 + 2H2O The HCl effectively removes OH-, which causes the Mg(OH)2 to dissolve to replace some of the OH- being removed by the acid. 
4. 
CO + 2H2 <==> CH3OH + heat 
Both a. and c.  
Adding CO causes the forward reaction to occur as the system tries to use up some of the excess CO. 
Removing CH3OH also causes the forward reaction to occur as the system tries to replace some of the CH3OH being removed.