Look at the function and see what it means. You've seperated the time and position variables. You could view the motion of each point as a function of time as an harmonic oscillator. (Some points don't move at all). Plot the function to see what it looks like. If you get some insight in the equation, the questions are very easy.
Plot your superposed function for t=0. Notice where the x-positions of the peaks are.
Plot your superposed function for (say) t=0.01. Notice where the x-positions of the peaks are now.
Which way did it shift? If 0.01 is too complicated, try t=(1/12)*(2*pi/w).
If it's not clear, try doubling the value of t you just used.
Presumably, you understand the meaning of "which way the sin(kx-wt) part travels"... and likewise for the sin(kx+wt). It can be seen as the direction along the x-axis of the motion of a peak. Apply the same reasoning to the superposed wave. You've practically got it... You just have to give the answer in the form stated above.
The second expression is easy to plot a graph of
"amplitude sin(x)cos((1/12)*(2pi)) [at time (1/12)*(2pi)] vs position x".
Can you numerically evaluate cos((1/12)*(2pi)), where pi=[itex]\pi[/itex].