try using rechargeable batteries. I've used the insignia for 6 years and have always used the rechargeable batteries, saves money. I use the Duracell recharger and Duracell batteries.
If random playback is the same as shuffle, then yes there is a shuffle function. It has a random playback setting "To a track, an entire CR of an MP3 album(folder)" according to the instruction booklet. I have yet to try that function.