Do all serif fonts have a slanted serif similar to the font illustrated in this exercise?
No. Serif is a very general categorization of fonts which can be further broken down into the board categories of: Oldstyle, Modern, Slab Serif.
The slanted serifs seen in this exercise are characteristic of Oldstyle typefaces. Among other differences, Modern typefaces have thin, horizontal serifs whereas Slab Serif typefaces have thick, horizontal serifs.