Except for EU citizens anyone coming to Germany to work has to apply for a visa (“Aufenthaltstitel”) at an embassy or another diplomatic representation of Germany in their country of origin (further information here: https://www.auswaertiges-amt.de/en/einreiseundaufenthalt/-/215870). In most cases a Schengen visa will suffice, if the stay in the Schengen area does not exceed 90 days. There is also the possibility of applying for a visa, which allows for multiple short stays in the Schengen area over a long period of time.
Social security for short term stays in Germany is payable in the country of origin.
Taxation: a so-called “Ausländersteuer” needs to be paid for musicians from abroad performing in Germany. If the band is organised as an entity or similar form of organisation further fees may need to be paid. An additional VAT might be added depending on the contract parties.
There are several recommendations for a minimum musicians’ fee but no legally binding minimum wage for freelance work. The Deutsche Jazzunion recommends 250€ minimum per musician for a concert and 500€ for festival gigs per musician although in practice many venues and concert organisers struggle to meet this requirement due to having no public funding.
A useful resource for information about details on taxation, visa, travelling with instruments, custom regulations (in German and in English) can be found here: https://www.touring-artists.info/home/ They have useful checklists, sample documents, and they also offer a phone helpline for individual questions, you can ask for a an appointment here: beratung[at]touring-artists.info
