Why do we use iodine to stain banana cells and methylene blue to stain cheek, onion, and yeast cells?

Cell staining is highly dependent on what components you want to highlight. For example, sometimes you want to stain the entire cell. Other times, you want to emphasize a particular component like the cell wall.
Iodine is primarily used to stain starches. Since bananas are plants, this means that they have a high starch content. So this makes it ideal for viewing such cells under a microscope. Iodine is also used for Gram-staining. Gram-staining is used to distinguish between two different types of bacterial cell walls: gram-positive and gram-negative.
Methylene blue has multiple uses. Based on the types of cells named, I’m going to assume it was used to show cell division and/or meiosis. In this case, it was used to stain nuclei. It is also used to treat many medical conditions such as hypotension, malaria, and methemoglobinemia.
http://terpconnect.umd.edu/~nsw/ench485/lab9b.htm

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3087269/