According to this: https://assets.publishing.service.gov.uk/government/uploads/... yes.

Note that the foundation has had a majority stake in RPi ltd (as a private company) for a long time this is not a new structure.

Yes, but as shareholders they must still act according to their 'purpose', which is a term in UK law that a charity can choose when it is set up as part of its charter, and then every action must be in accordance with.

Purpose of spinoff = get dividends to fund the original purpose

Non profits aren't generally charities.

Yes. large non-profits can need to invest a lot of money.