Oddly enough when a fleet is in sleep mode we get a notification if they see an enemy fleet however if the fleet is in guard mode we lose this information and when we are managing a big empire we often miss a few small ships that pass through our defenses and start being annoying in our home systems.

An option to allow notification for ship in guard mode would be most welcome

Yes, that would be awesome to have notifications that there is someone in the system your fleet/ship is in.

When there is action going on around whole map, it is becoming quite a chore to scroll everywhere just to check if there are any bugs to squash.

nothing wrong with that idea at all

If not already, give it a chance in the Idea section :)