Copyright and related rights management bodies are differentiated by European law into collective management organisations (CMOs) and independent management entities (IMEs) intermediate for collecting fees from the economic exploitation of copyright and related rights. Using a work and phonogram requires the authorisation of the rights holders and the eventual fee payment. Collecting societies are responsible for 1) issuing licenses, 2) collecting the fees, and 3) redistributing the royalties to the rights holders. Be aware that as an author/performer, if you are not a member of any related CMO or IME, you would not be able to receive the royalty deriving from the exploitation rights collected collectively by them. Note that music publishers are entitled to manage directly only the exploitation rights which are not managed by CMO or IME.
The European CMOs are usually competent in managing both performing rights and mechanical rights; while Anglo-American PROs such as ASCAP and BMI in the USA manage only performing rights and the mechanical rights are managed by Harry Fox Agency (https://www.harryfox.com/). Since Harry Fox relates only with publishers as its member, under the Music Modernization Act of 2018 the Mechanical Licensing Collective (MLC), a nonprofit organization, is established. MLC collectively intermediates the digital mechanical royalties deriving from music streaming which independent music creators (songwriters, lyricists and composers) can collect directly.
Collecting management organisations and independent management entities usually enter into reciprocal representative relationships with other CMOs or IMEs worldwide to ensure that their members' royalties are collected globally and duly shared. In any case, the members are entitled to limit the CMO intermediation to certain territories and type of rights.
Yes, you can register with any CMOs or IMEs worldwide to provide licenses and collect royalties for the exploitation of your copyright and related rights.
Any exploitation of a work and/or phonogram is subject to authorisation by the rights holders and eventual payment of royalties unless it falls under an exception or limitation to copyright or the work and/or phonogram, is in the public domain.
CMOs and IMEs are mandated by the rights holders to deal with certain categories of rights. For other types of rights, the rights holder directly grants authorisations and collects royalties.