For the botnet: having zombies charge the AI, ever, tends to result in nasty unexpectedly-freed-ships problems. For some players that's fun, for a lot of them it's not.
I do see how it becomes a problem when it can destroy an effectively unlimited number of enemy ships, not to mention establish a nearly endless protective force. Eventually that erodes the fun of the game because it becomes a matter of "Get a botnet or two, get something that deals with the relatively few things a botnet can't handle, win game" and some players will feel like they have to get a botnet if it's there or else they're not playing optimally.
On the other hand, I don't want to lower the number of valid strategies players can pick from. That just leads to one-way-to-play-the-game from a different angle.
That said, I think one of the suggestions will help contain part of the insanity: have a max of 2000 zombies on the player team (4000 on high caps, 1000 on low caps). I think the botnet is the only way to get player-allied zombies, so that would work, I think. The AI needs to not have a zombie cap for other mechanics, but it doesn't appear to be getting that kind of use out of the botnet anyhow.
For the other part (the botnet's personal ability to accidentally waves), I think the problem is that the dps is basicallly... infinite. 10,000,000 * 50 every 2 seconds. 250,000,000 dps. That's twenty times what the buffed arty golem has, and applied more efficiently. No bueno
Actually, it's more than the Devourer on-paper (which has same base power and 2-second salvo time, but 45 shots instead of 50), but I think there's something about the devourer that actually makes it automatically kill whatever it hits (I once made the avenger mkIV briefly to put it in a fight vs the devourer, and the fight was over before the devourer's first salvo was done hitting). For reference, the armored golem does 500,000 * 4 / 2, 1,000,000 dps. Personally I'd like to bumpt that up a bit, not because it's not balanced but because I want to raise the overall "balanced" bar for golems. Not sure if that's the right way to go, though.
Anyway, not sure what the answer is. Could leave dps the same and see if the zombie cap is enough. Could lower the number of shots to 10 as suggested. Or perhaps could reduce the damage per shot to 500,000 or something like that: an advantage of this is that if it doesn't kill something, and something else does kill it, it's "normal reclaimed" instead of "zombie reclaimed". That could lead to bug reports if people see normal reclamation happening while they have no normal parasites in the fight, however.