Whether it's used privately or otherwise you will need the boat to be licenced plus you will need a licence to fish (yes, even with a rod). Not only that but everyone on the boat, whether fishing or not, must have a licence. Port police are the people to contact for full information. The fishing licence is not expensive - around €25 for two years, I think. No idea about the cost of the boat licence but you have to take a test administered by Port Police (or possibly Coast Guard).
The Coast Guard do check even very small boats for safety equipment and size of fish caught. They apparently get very stroppy if you have anything undersized. If you get caught without the necessary papers fines are huge and it has been know for boats to be impounded until the fines are paid and every bit of safety kit you can imagine has been provided.
There have been one or two threads on the forum previously so it may be worth searching the archive.
I don't know the specifics about diving but there are some pretty stringent regulations about location.