Just chiming in here: there are at the moment some problems with federation. I’m an admin on LW, and generally we remove spam pretty quickly but it currently doesn’t federate quickly. We are working on solutions that temporarily fix it till the lemmy devs themselves fix it.
As mentioned before there is indeed an API. Please keep in mind that some instances have rules on how to run a bot. On lemmy.world for instance you need express permission from the mods of the community you are using the bot in, you should obviously mark the bot account as a bot account and the name should make it clear that it is in fact a bot.
FYI: admins can see all reports. We currently have a tool running that scans for posts that are reported a lot, which will then notify people who can do something about it.
Sorry, I don’t completely get what you mean with this sentence
As far as I understand, removal by mods is federated and will thus be visible on all instances in the modlog. But not an expert by any means.