My dc is in the third semester of an undergrad degree in Germany, so assume many of the same issues apply.
Living costs are hugely cheaper than in the UK. My dc is in a big city that is not one of the hotspots like Berlin or Munich, and is paying €260 a month for a large sunny room in a hall of residence. That includes all bills and wifi. Private rentals are more expensive, and they will have to fanny around with bills and things like TV licence, which can be a faff, although all doable with persistence. Private rental for a room in a shared flat in my dc's city would be around €350-450 - WG-gesucht is the DE equivalent of Spare Room. https://www.wg-gesucht.de/
My main tip would be to apply as early as possible for a room in a Studentenwerk accommodation, as that will be financially and administratively the easiest and best option. They tend to be organised in flats rather than just rooms off a corridor, with a small shared kitchen and bathroom - larger flats generally cheaper per student than smaller ones, so that might be a way round the potential for isolation.
If you're sure there are no fees for a free-standing masters (do check, as there's no fee for a masters following on from a bachelors, but likely to be different for a free-standing masters), then the main cost will be the Semesterbeitrag, which will be in the region of €250 per semester. This is a contribution to the subsidised facilities the uni provides, and is actually a terrific bargain as the student card acts as a pass for 6 months worth of public transport in the city and wider region. It also covers things like the Mensa (subsidised canteen) and sports facilities etc.
Does your dc have German citizenship? That's the thing which makes the biggest single difference in terms of easing the administrative burden, as is having at least one parent or close relative who understands how German bureaucracy works. This is much more burdensome than it woudl be in England, and some things have to be done in a particular sequence in order to unlock the next level of the Living In Germany game.
The main admin hurdles are:
Health insurance: the uni will need to see proof of health insurance before they will register him. The EHIC or GHIC is not really designed for longer stays abroad, but you CAN use it for this at least in the short term, as long as you don't have pre-existing conditions needing ongoing treatment. You will need to take the university Zulassung (the provisional document stating he has a uni place) along with the GHIC card, and your passport and proof of address etc to a branch of a state health insurance company like AOK. They will then issue you with a piece of paper which confirms that you are exempt from the requirement for health insurance, which you in turn supply to the uni in order to get registered. Some of these things may need to be done in person with a physical signature, or via fax. Yes it's ridiculous, but faxing is still very much a thing in DE.
Once you've secured accommodation and have a rental contract to that effect, then he can do the Anmeldung (register with the local authority). If it's a Studentenwerk accommodation, you may need the Einschreibung (official uni registration) or at very least the Zulassung in order to secure the accommodation. The Anmeldung is crucial as you cannot do anything without that, eg. open a bank account or get a SIM card. If he has ever been angemeldet in Germany before, you will need the Abmeldung ins Ausland, otherwise the computer may say No.
Anmeldung takes place in the local Bürgeramt or Bürgerbüro, and they generally have an online booking system. Do this as far ahead as possible, and in any case before the mad rush for the start of the Semester when getting an appointment slot in a university city can be like trying to score Glastonbury tickets. With the Anmeldung you can unlock all the special features of Living in Germany like getting a phone and a bank account - Sparkasse do a bank account for students that doesn't charge fees (most banks do charge).
Do ask if you have other question! DC is having a brilliant time, and would highly recommend the experience. :)