Can someone give a blessing to a sick friend, or a birthday blessing, a blessing at a meal, or on other occasions? Does the person need the permission of the local bishop?

Yes, laypeople may give the types of blessings that you describe. Extraordinary ministers of the Eucharist, for example, can bless people who come up at Mass with arms crossed over the chest, usually indicating that they are not Roman Catholics. Anyone can offer a blessing at the start of a meal or at its conclusion. The same is true for visiting the sick or celebrating someone’s birthday. I once visited an Irish American household where each person was blessed with holy water before leaving that house. Such blessings remind everyone that God is the author of all life.

Because some blessings are more public, they are normally reserved for priests, deacons, or bishops. Ordinarily, one of them is the Church’s official witness at a wedding or presides at a funeral outside Mass, but the local bishop can designate a properly trained layperson to be the Church’s witness in either of those situations. The blessing of churches, altars, chalices, and patens is normally done by a bishop.