1. Yes, I use them in my Rome campaign. Bobbin's unit card mod is helpful, telling you how many artillery pieces you get. The big stone thrower is utterly useless - one artillery piece, so it barely breaks through a stone wall's gate with its last ammo. The smaller stone thrower unit works well though, easily gets you through a stone wall with ammo to spare for suppressing nearby wall towers if need be (2 artillery pieces makes all the difference). Similarly I favor the lighter bolt throwers since you get 8 artillery instead of 4 for the heavy bolt throwers. Not every legion has artillery, but many do. Usually a light stone thrower in a city near a potential enemy, and a bolt thrower with legions on or near a frontier (standing on the bridge next to Tarsus, for example). Note that stone throwers won't get you past a heavy stone wall, so artillery can be mostly useless in Hellenic and Eastern territories. The Celts/Lusos/Germans can't build beyond basic stone walls, so stone throwers are useful in the west. For some reason the AI rarely fortifies the eastern Mediterranean coastal cities (Halikarnassus through Sidon), so that's a good use for them too. Raiding Antioch and burning it to the ground in a single turn was fun! That would be the main answer to your "why use them" question - take the city instantly, before any nearby armies can interfere. Particularly when raiding enemy homelands from the sea, as in the Antioch example. I haven't tried it yet, but they may also be useful to force those massive central European rebel armies to besiege you in the city they were supposed to defend, rather than fighting you in the open field.
As Rome, the enormous cost of artillery is a virtue, not a flaw. Factions like Baktria will obviously disagree on that point.
4. I think it's random. A few percent per turn seems typical.
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