did the Soviet commanders shoot their own troops

Yes, as did every other country during the war. Some more than others, but there wasn't a single country in WWII where officers did not shoot their own soldiers for insubordination.

and send them into fights without enough guns and ammo?

No, this is common propaganda pushed by COD and Enemy at the Gates, based on a single officer's report from the Battle of Stalingrad that they did not have enough guns to equip his troops. Conveniently, the second half of the officers report is usually left out, where he states that he is diverting his troop ship to a supply depot to rearm before heading into combat.