No one here is able to answer what is or isn’t allowed by the EULA. People here can only guess. Only CCP can really answer that. Any automation that gives an in-game advantage have a chance of being considered a breach of the EULA. So, if you want an answer that holds any weight, you will have to contact costumer support and ask them.
Take into consideration that live “reading from screen” might count as automatic interaction with the client, which is forbidden.
Making a screenshot every few seconds and analyzing this might be okay, but I would ask the GMs about it, as it also is some kind of automation. But I wouldn’t use it anyway, it would cause serious stutter and will quickly fill the hard drive, unless you immediately delete them again. But thats a lot of read/write access.
You should take a look at this program:
It analyzes the logfile that EVE creates from your combat messages. This is no interaction with the client and causes no issues with lag or stutter. It simply reads out the damage amounts (incoming/outgoing/neuts/remotereps) and with the timestamps it calculate the average DPS over time.
But in this logfile are also the names stored of anything that tries to hit you or anything that you hit. So you could use this information to quickly assemble a list of everything on the grid, since after like 10 seconds everything should have shot at you at least once. You could even go a bit deeper, looking up all NPCs rate of fire and estimate an amount for every type, depending on how often they appear in the log over a set timespan.
You will find the logs under PC / Documents / EVE / gamelogs