Best to contact the embassy first.
More than 90 days.From what I guess If visiting any EU countries from the UK for more than 90 days total within a 12 month period will require a visa for that country. It will probably require visiting the respective embassy in London for an interview, same if you want to visit any other countries, you will need to declare any criminal convictions etc.
Contact the embassy first to see if your required to make an appointment.
If you want to work during you stay you will need a work permit and that will most probably only be available if the job requires a skill that is in short supply. For instance it’s unlikely you will be entitled to a work permit for unskilled work eg Bar work, retail etc.
You will be forbidden by law from working if you don’t have a work permit.
You might have to prove you have sufficient funds to cover your visit, proof of where you will be staying and proof of your course acceptance.
90 days or less
At present as of Jan 1st 2021 if you’re visiting for less than 90 days then you will not need a visa but some kind of Visa waiver will probably be required in the future similar to the US ESTA. Most probably you will be able to do it online and will not need to visit the embassy. It’s possible in future that you may have to show proof that you have sufficient funds to cover your stay and where you will be staying.
Again you must NOT work at any time unless you have a work permit!
Only the respective embassy can answer your question correctly.
You’re just lucky to be one of the last generation of students entitled to Erasmus.
If you want my opinion I think Brexit is bloody madness