What proof should be provided (and when) if a partner expects to receive a grant to cover all or part of the 20% co-financing (convention, agreement…). If the grant is not certain, is it possible to indicate that the 20% will be covered by self-financing, even if it means receiving the grant later?

The only document to provide is the partner declaration signed after the project submission.
In this document partner must ensure to have the related contribution to cover the 20%, declaring it as own funds with the possibility to modify with another private or public co-financing source later.