1. From the screenshot it looks as though the landowner on the opposite bank is also the landowner of your side of the watercourse. The red dotted pattern indicates that their property is registered with the Land Registry. Next step is to pay the €5 for the folio details on landdirect.ie and see if that gives you a lead on the landowner.
2. The Land Registry map includes a disclaimer regarding exact boundaries but in this case it looks clear that the landowner on the opposite bank on both banks of the watercourse.
3. Definitely highlight the issue to the Council.
Longer term it could be work getting the end of your property reinforced either through natural (e.g. willow) or engineered (e.g. rock armour) means.