Re: Changing speed.
Difficult to know from here... Here's a step by step... but it this doesn't help, please make sure your audio regions are set to "follow tempo" (in the Region Parameters area in the Inspector).
1. Click on the Global Tracks disclosure arrow to open the Global Tracks.
2. Click on the Tempo tracks disclosure arrow and/or resize it from the track headers boundary.
3. The line displays the current tempo of your project. Double-click in an empty area to create a node (and tempo change) at that point.
(Repeat this step to create as many tempo changes as you need.)
4. Position the mouse cursor over the line and drag up/down with the hand tool to choose a different tempo for that section of the project.
5. Position the mouse cursor over a corner created as a result of the tempo change (not a node you created) and Logic gives you the finger tool.
6. Drag this on the horizontal axis to create a curve in the tempo change.
If you still have issues getting this to work, please let me know your process with as many details as possible... i.e. what do you mean by "the tempo doesn't stay?" The regions play back always at the original tempo or the tempo of the project reverts to the original setting?