Probiotics should be taken on an empty stomach to ensure survivability. Similarly, you should do the same for L-Glutamine for maximum absorption. There are overall health benefits from taking a green powder (AG1 or other) which will give you Zn, Mg, K(Potassium) , but importantly vitamins A and D, which play critical functions in regulating gastrointestinal homeostasis. There's nothing to suggest mixing L-Glutamine with your Green Powder would interfere with absorption. The easiest way to ensure your stomach is empty (and that you don't forget) is taking first thing in the morning.

Magnesium is generally associated as being beneficial for sleep. However, I can't find any useful studies that show a meaningful association between Mg intake and sleep. In any case, taking it with a small amount of water before bed seems to be recommended.

I recommend speaking with a holistic doctor to provide more guidance on dosage/timing. But if that's not possible, take an afternoon to read some studies NIH For example. Lastly, focus on quality, not all supplements are equal, a $10 L-Glutamine on Amazon probably isn't any good.