Hi when you play, do you just blow from your mouth but imagine the sound coming from elsewhere? How do you exhale the air through your instrument?

Blow from yor diaphram and breath from the sides of yor mouth.

Yeha, use your diaphragm and breathe from your mouth by opening it slightly and take a quick breath. Don't breathe from your nose.

As my past band director said, "Never from the chest but from the stomach." She also said, "Imagine the spirals of air comming out from the bell."

yeah, use ur diaphragm (if u don't get it, it means that whenever u take a breath, ur stomach swells instead of ur shoulders rising). And don't breathe thru ur nose, instead take short breaths thru ur mouth (and make sure u dont lose ur embouchure in the process). Good luck.

I know that you should breathe with your diaphragm, but why with your mouth and not your nose? I just use my mouth because it seems more natural, but what's wrong with the nose?
Also, how can I blow for longer, because I always run out of breath in pieces, but I can hold a long note for 30 seconds.