Sorry to neglect details. I am running PRE 12 and Windows 7.
What version of Premiere Elements, what computer operating system?
Right click the audio clip, from the pop up menu that appears, select Fade, followed by Fade In Audio.
Then right click the audio clip again, from the pop up menu that appears, select Fade, followed by Fade Out Audio.
When you do that, you will generate two Volume keyframes at the beginning of the audio cip and two Volume keyframes at the end of
the audio clip. These keyframes will present on the Timeline as white dots. These dots can be moved with the mouse cursor to customize
the Fades at the Timeline level (see audio clip's rubberband - orange line that runs horizontally across the duration of the audio clip).
If you need some screenshots on this, please let me know.
If you do not see the rubberband "white dots", right click the clip, select Show Clip Keyframes and click on the appropriate Volume path. Expand
the Timeline content with the -+ slider to get a better view of the Timeline content.
Please review and consider.
I saw your post right after I clicked the Add Reply button for the post 2.
The details would be applicable to Premiere Elements 12/12.1 Windows 7 64 bit.