Immersion has 4 wires instead of 3

It's Certainly what I would consider a grey area. When someone is asking basic questions about such a critical item then they have no business messing with it.

You asserted that the OP "by not calling an electrician … have broken the law and undoubtedly invalidated your house insurance if it causes a fire." That is a bold statement, that doesn't stand up to scrutiny. It is a like for like replacement and is most likely categorised as a minor work. (I say 'most likely' as the authors of the applicable documents could have been more clear.)
The issue of a fire is different. There is a requirement for anybody doing electrical work to be competent (again, no definitive standard set). If the fire could be shown to be due to a poor quality installation, the installer could be held liable. If the installer was, and remains, RECI registered then they should have adequate liability insurance to cover this.
You also asserted that "There are some things you are simply not allowed to do unless you are qualified, and anything to do with water heating is one of them." Other posters on Boards.ie have stated that they got written confirmation that replacing an electric shower is considered minor works. If true, and I fully expect that it is, this point also fails scrutiny.

Look, there is a broad consensus that the OP's lack of basic knowledge meant that they shouldn't be doing this work. That is a long way from suggesting that only a RECI registered contractor should do minor electrical works. However it is certainly wise to recommend caution, as other tradespeople may not have liability insurance should issues arise.