(Not a Teacher)
1) If a warehouse full of volatile chemicals were on fire, I'd assume the firemen would be standing back in case of an explosion. However, if this were, say, a bomb threat, the firemen would be standing by as the EOD team did its sweep in case there was an explosion. The context is a tad important here.
2) If I were going to use 'stand around' in that sentence, I would provide an object to stand around. ("He told the students to stand around the desk so they could see the experiment.")
'Stand around', without any further context, means 'to loiter'.
'Stand back' makes sense on its own here.
- For Teachers