Allow me to attempt to answer most of your questions...
2) I don't know about Origins, but in LC and RoR the answer would be no
3) Larger territory and for solo play, the beasts and criminals along with boss sized creatures take the place of the other faction. You also can play with more than 2 players in LC, but I don't recommend it.
4) RoR offers Titans which bring a unique flair to the game and are much more difficult to beat.
5) Chip expansions provide better unlockable crowd favor chips and different troop for each faction with different abilities. Also some different equipment, and in some cases, more Titans and senario based enemies (look up Army of One).
6) If by "arenas" you refer to the ones provided in Origins, I don't know, but with the other games, you are always able to add them in. Hoplo is sort of "sandbox-y" that way. The Traps are baked into the LC map with enemy spawning points. Don't be standing on one of those when a beast or criminal spawn.
7)Again, in Origins, I'm not sure. In LC and RoR, no. There are 2 hexes on a 3rd Kickstarter backer arena that you couldn't move on to at all. You have to walk around them. But no terrain in the sense of inhibiting movement.
8) Yes, there is equipment in the crowd favor chips, and elsewhere through the factions and such. There are also chips you deploy onto your units that give "buffs" to certain attributes.
9) I have almost all the extras up to Origins, and only stopped because I ran out of room to get everything in one box (I affectionately call it "My 12 pounder"). And I still want to purchase Army of One. I have also considered getting the two latest factions, but again... no room.
It is dead simple to mix everything. Is there any reason to? That just depends on the kind of gamer you are. I would say that it certainly worth getting either the two big box sets or one big box and several chip packs.
10) Yes. The way you described it, is essentially how it works. Of course there are several variants. Again, it's kind of a "sandbox-y" game.
11) AI differs from thing to thing. Beasts are random movement but brutal fighting (once they are adjacent to a players chip, those two or three or four are locked in battle until either the beast dies, or the player's units die). Criminals always head straight for your Hero chip (the number of spaces 0-2 is decided by dice roll). Bosses move either like a beast or a criminal and have a super power that may or may not trigger thanks to a dice roll. Titans... well there are too many things to explain because each is entirely different. All dice rolling though.
I hope that sheds some light. I have had this in my collection for over 3 years and I still have a great time solo and pvp. It is easy to learn and teach. I would say it is well worth the effort to get your hands on.