Can you use triggers to order computer player units to do things like, nuke, attack a certain target or/and burrow?
You can use the 'order' action to order the computer move, attack a buildings, or move& attack.
You can also use the AI scripts to tell the comp to enter men into bunkers, enter men into transport (shuttle, dropship, overlord) and to nuke areas.
You can't order the computer to attack a spacific unit if it's not a building or burrow units.
Here are some tricks to make it seem that way -
Attack a spacific unit: give another player the same color of the player in SF and set the other player to enemy with the attacker. than give the unit you want to be attacked to the foe player.
Burrow: create a sibling burrowed unit for the one you want to burrow in an unused part of the map and create a detector and an attacking unit near the sibling, wait for 2000 miliseconds or so and replace the sibling with the original units.
Burrowed units automatically unburrow when they get attacked, and will burrow back a short time later if the attacker is gone.
We do have a tutorial on nuking if you need help.
http://www.staredit.net/index.php?tutorial=55And there is no way to "make" a unit burrow right now. Though as AqoTrooper stated, you can replace the unit with a burrowed one to make it look like it burrowed.
also, if the comp's ghost see's a enemy unit, it will attack it even if it is being ordered to nuke it.
Not if it is in the middle of nuking

Didn't I say that? I thought I did, if one is willing to read betweent the lines