I'm assuming that when retrieving a meteor for study and later display, there are precautions taken against possible radiation coming from it. Is my assumption correct and are there other precautions taken such as protection from biohazards? (e.g. is it not possible for a meteor to carry a foreign viral agent?)
Meteorites are composed of rock and iron. They are not radioactive, at least no more so than any other stone. A banana is probably more radioactive than a meteorite.
You do not need protection for foreign viral agents either. Meteorites are stones that have been orbiting in space, usually for billions of years. They do not contain any living things. The have also passed through the atmosphere so fast that their surface can begin to melt from the friction.
You can pick up a meteorite with you unprotected hands
For pedants: A meteorid is "space stone". Meteor is the flash of light in the sky as a meteoroid passes through the atmosphere. Meteorite is the stone from space that you find on the ground. It is the meteorite that you retrieve for study.
There is a suggestion that ancient meteorites bought the ingredients for life to Earth, or even seeded life on the planet, but it is speculative as we don't have the evidence to prove it.