My colleague Darren (@1318980) has written a very nice SimWiki post on the turbulent boundary conditions which can be found here: Defining Turbulent Boundary Conditions - it explains how you can calculate the turbulent kinetic energy as well as the turbulent dissipation rate.
If you are interested how the solution behaves over time you can use the transient solver. However if you are only interested in the final solution (no historical reference intended) you may use the steady-state solver. One thing to notice though is that you have to roughly know where/when the steady-state is meaning that if the time to reach steady-state is larger than the simulation time, the transient solution and steady-state may vary.
For convergence I am not very sure how this affects the behavior. Sometimes the steady-state solver converges faster then the transient one neglecting higher order terms involving time-dependent terms but for some cases opposite behavior can be seen. Tagging the @PowerUsers_CFD here to give you additional information on your questions and correct my statements if necessary.
It would also be nice if you could share your project as well as the values you obtained in FLUENT. We will help you out here!
Cheers and all the best!