For people who have questions, please put them here and I'll use those to help formulate... something... for a tutorial. We'll get to that later. For now just knowing the questions will help later define what the added in-game stuff will be to help give you the same information in a better format. Note this thread is for questions only, not suggestions.
Cyborg: on the city map, where am I supposed to go? I have just been picking whatever sounds good and playing those maps.
That's about the size of it, really. You aren't out to go anywhere, you're out to improve yourself or weaken your enemies as much as possible during the 50 days (or less if you attack robot command stations). But there's no one place for the final battle that you have to get to, or anything: the robots are coming to you!
Cyborg: as I am moving my robot through a level, there are explosions going on. My enemy seems to be self-destructing without my doing anything. Is that normal?
It may be that there are some razorbots out there attacking the other bots, or that there are some mines that enemies are stepping on. If I could see the level in question, that would make it more clear.
Cyborg: is only one robot active at a time? It seems like I would always want to use my assault robot to move around and only switch if it makes sense. If it's not true, that means I should be able to do 4 attacks.
Correct, only one exo is out at a time. Switching exos costs a move, so if you get into engagement range and then try to switch, that's tricky. But you can indeed do what you described, simply by using the 6-9 keys on your keyboard, or clicking the portraits, whatever you find is quicker. Definitely don't hesitate to switch exos to the best one for the job!
Cyborg: I don't know where I'm going in the levels. Just going in a given direction. I don't really know my own strength or that of my enemy, so I haven't been lasting very long.
The tooltips can give you a good idea, but basically assume that you cannot take return fire -- almost all the time you want to avoid that. So use Whistle and use the Wait commands (spacebar for the latter) to let the enemy come into your range, then blast them before they can hit you.
In terms of where to go in a level, the tooltip gives you an idea of your objective, and then it's a matter of you exploring to find it. Or in some cases, you're just there to kill everyone.
Cyborg: Absent a tutorial, just need a little guidance on where I am supposed to be heading on the map and what I'm looking for in the levels. And should I be going all combat or avoiding the other robots? They seem to be kicking my butt really quickly.
Hacking locked doors for loot can be a really good idea, but otherwise just getting to the end with as many exos intact as possible is good: you get more loot the more exos you have suriviving at the end. In terms of combat, your goal is to generally take no fire from enemies. So kiting them and sniping them and so forth is typically good. If you rush into a room with many enemies, that is very dangerous. Bottlenecking them as much as possible is a very good thing.