Hayder - it depends on the institution but I would argue 'of course' - where possible. Most institutions would realise that it is in their best interest (research rankings, government funding criteria etc) all around to support research. Many institutions offer 'internal' grants, 'start-up' grants and early career researcher incentives (grants and internal/external professional development workshops/courses) as standard. Institutions also often look to develop 'research clusters' of research strengths and expertise that mentor emerging researchers - as well as support their research leaders. Some disciplines more 'naturally' thrive in such an environment i.e. Medicine - but the intention is usually to target all disciplines.

Yes, for my institution.

Yes to financial, no to moral. You have to provide your own moral support because, sadly, most people will be negative about other people's research