-Was barbed wire placed in no man's land, or only directly in front of trenches?
-If wire was placed in no man's land, were there strategies for efficient layouts? How did they decide where to lay the wire?
-Was it used it combination with minefields- if so, how?
-How did armies ensure that they could advance through their own wire safely?
Using the Canadian War Museum's PDF about barbed wire, it served four main purposes:
"to delay enemy troops while they were under fire
to restrict the enemy's capacity to manoeuvre
to force enemy soldiers into zones where they would be most vulnerable to defensive fire
to disorganize enemy attacks"
The barbed wire was often set up in a way that created "kill-zones" for enemy troops, letting the defenders concentrate their fire on smaller areas, thus making them more effective. The wire was typically laid in no man's land ahead of the trenches to provide these zones.
It was imperative that the soldiers laying the wire did so in absolute silence, so they would not be discovered and killed, and both sides developed "silent" posts for supporting the wire that could be screwed into the ground, as opposed to being hammered in, which created a lot of noise.
Unfortunately, I cannot find any good sources on combined land mine/barbed wire use at the moment, so I'll let others talk on that topic, instead of speculating.
The forces that laid barbed wire would know and have mapped out the "safe" routes through the wire on their side. This was crucial as it allowed them to get away from their trenches quickly, without being as likely to get stuck in the wire they had laid.