Can this be done

I am just learning WP and I don’t want to waste time trying to do something that can’t be done. My customer want the home page to have links of categories. When the categories are clicked then the next page is the most current post of that category. A right sidebar has a list of the ten most current post titles for that category, which when click loads the post in the main column. There needs to be a search box in the right sidebar also to find all articles and list the titles in the right sidebar.

Can this be done? If so what templates would be use for each page.