It's all just a dream
You're asking a couple of questions, but they can all be answered with a single answer: the dream messenger isn't really going anywhere, and the person whose dream they are visiting is asleep. From the spell's text (emphasis mine):
You, or a willing creature you touch, enters a trance state, acting as a messenger. While in the trance, the messenger is aware of his or her surroundings, but can't take actions or move.
If the target is asleep, the messenger appears in the target's dreams and can converse with the target
So, by the time the messenger has entered the dream of the sleeping target, neither the messenger nor the target can take actions or move. The messenger can't take actions or move because the spell says so, and the target can't take actions or move because they are unconscious.
Since neither creature can take actions, this means no spellcasting, no attacking, no using items, or much of anything other than what the spell itself allows. Furthermore, the caster of dream isn't actually traveling anywhere, so the target of the spells wouldn't be in range even if you could cast the spell you want to cast. Lastly, since the dream isn't real and no one is physically present in it, no one can die or be harmed in the dream.
You can do anything you can dream of
So basically, the only mechanical effect that the dream spell can produce is the "spawn a nightmare" feature. However, beyond that, the messenger is free to shape the dream in whatever way they please. It won't let you directly read the target's thoughts, but if you're clever, you might be able to come up with a dream scenario that will fool the target into unwittingly revealing you want to know.
For example, suppose you're planning an invasion of the BBEG's fortress, and you want to know what defenses the BBEG has prepared. You might concoct a dream scenario where you pose as the BBEG's lieutenant. You report that the party has been sighted approaching the fortress and request orders. Hopefully, the BBEG will fall for it and start issuing orders like "man the cannons", "prepare the boiling oil trap", "release the basilisks", and so on, thus giving you valuable information on what defenses to expect when you invade for real.