The word "protist" is used as a catch-all to describe incredibly diverse single-celled eukaryotes. There are protists related to plants, protists related to fungi, protists related to animals, and protists that form their own distinct lineages.
Symbiosis: How do cells from different branches of life interact? What molecules are exchanged? What mediates their interactions?
Biomineralization: How does life concentrate elements to seed and control mineral formation? What is the function of the complex forms created?
Evolution: How can studying diversity inform us of the link between information (DNA sequence) and form and function (phenotype)?