Advice on TAX and HEALTH INSURANCE? Irish/UK living in Germany.

As EU citizen, you have the right to settle freely in Germany.
However, you must register your residence and fulfill all requirements like normal (German) residents.
That means, you need:
- A place to live (e.g. rental or bought property - fake or "pro-forma" registrations are not allowed) that you register with the local authorities.
- German health insurance (read related threads about the options available, and costs)
- You must submit a yearly tax declaration and are taxable on your world income - unless otherwise determined in a bilateral tax treaty with the country where you earn (check what the UK-German one states and whether it survives Brexit at the end of the year - it is possible that you are double-taxed then!)
- As self-employed, you must register your business with the relevant German authorities, too. There may be licensing or other certifications needed and you must fulfill German accountancy rules.