Adding a pause (delay) to a Keynote slide?

Welcome to Keynote, bryanus -- it really is a fantastic application.

If you have the slide show looping as a "Self-playing" presentation, there is no way directly to adjust the timing of the separate slides -- the slide transitions after all the builds are done, with whatever overall slide delay is set. However, there is a workaround for this, which is to put a second build of a transparent object on the relevant slide, and using the Build Order drawer to adjust its timing relative to the first build. In this way, the second build will control the "pause" after the first, but because the object is transparent, it will have no visible effect.

As for the exit/enter effects you want, you can do this with a Push slide transition, which will look like one slide is pushing the other aside. If you want to keep it all on one slide for some reason, you can also use builds for the individual slide elements, with the exiting elements using a Move Out, and the entering a Move In. This solution is more complicated, as it requires setting the timings for all the elements individually, but it allows for some different effects, such as an entering element appearing to push its exiting counterpart directly, rather than the whole slide moving.

The pause is easy: Just set a 5 second (or whatever you choose) delay in the
Transition window of the Inspector. OR, you also could have it Transition on a Click, rather than Automatically if you don't need it to run unattended.

Exit Stage Right and Enter Stage Left are two separate operations that can be accomplished simultaneously with two Builds, but only within the same slide:

1) Create two separate slides - one with the first information, another "temporary" slide with the second. Then, on each slide Select-All and Group All.

2) On the first slide, select the Group and assign a Move-Out Build (choose left-to-right).
3) Copy the Group from the second slide and paste it into the first slide; select it and then assign a Move-In Build (again, choose left-to-right).
4) In the More Options drawer, have the second Build occur Automatically with the first, with no delay.
5) Once this works, delete the "temporary" slide.

This should do it.
Good luck.