*Do we need to learn any special skills before going night diving?
Taking AOW couldn't hurt, but at the least I'd try and read the night diving section of the book or search around here for tips (though they'll likely all get repeated in this thread.) There's lots of little tips like like not shining your light in your buddies eyes and blinding them. How to signal, that's different.
*Do we need to go through any training first?
Need, no. I see people on boats all the time doing their first night dive, they get a good briefing then off they go. I don't know that I would want my first night dive to be completely on my own with a buddy who hadn't done it either. You could maybe rent a DM for your first night dive, or maybe you can find a find guided night dive to go on. Or find some folks who will let you tag along (but don't push if they don't really seem to want to - some folks will enjoy taking a newbie on their first night dive and some will not be comfortable with this.)
*How much different is it from day diving? IOW, what should we be mindful of?
Well, it's dark.
It may creep you out at first, or not. There is a bit more task loading, from using a light if nothing else. One hand will be occupied with that. Depending on your gauges/computer you may have to illuminate them. You will see different critters, and you will probably focus much more closely on smaller area of reef.
*Aside from your light(s) going out, is there anything else that can go wrong that's specific to night diving?
Buoyancy control is something to watch out for - even if you feel you have this nailed down, without as much visual reference you may find that you really don't. Watch out for floating up or crashing. Be careful of knocking into things in general, have to stay aware of what's around you, that's harder in the dark.
*Do we need strobes to mark each others' position?
You don't need them, but it doesn't hurt to have a marker light and if it makes you feel more comfortable why not. I am against using strobes for this though, as they can be annoying to have in your view at close range as well as to any other divers in the area. (If you were on a boat dive, they often mark the anchor line with a strobe, so strobes on people can be confusing to others a distance away in that situation.) You can get constant on marker lights pretty cheap, no need for glow sticks.
*Since we'll be shore diving, do we need to mark the entry/exit points with something? (I don't think the Bonaire Marine Park allows glow-sticks)
Sometimes people put a light or strobe someplace, like tied to a mooring line or whatever works, occasionally we have. (A better use of a strobe than on your person, IMO.) But if you are diving from your hotel in Bonaire, most if not all have a line running from the dock to the dropoff and down the slope. You will see the line on your way back, it's pretty hard to get lost, even at night.
*I know we'll need a primary and backup light. Is LED technology good enough yet?
For tropical diving they're certainly fine, I wouldn't bother buying anything other than LED at this point. Just too many advantages.