Will at CT scan or MRI pick up a parasite?

In many instances. Usually we see the results of the body's reaction to the parasite, rather than the parasite itself. Parasites such as cysticercosis can deposit material which en sites the body to react - for instance in the brain. In other situations a byproduct of infection such as an amoebic abscess in the liver can be identified. Virtually every organ system can show the result of parasitic infection.
Maybe. It may, especially for worms depending on the size and if it's in its cystic form. Other times, it is picked up indirectly by the way the image enhances when contrast is injected or the effects it has on the surrounding tissue (eg localized edema).