"Princess Phone" was a style of telephone that was popular in the 1960s and 1970s. The phone had a small, narrow design. Blanche was talking about having a skinny body with good muscle tone, and Dorothy was teasing her by suggesting that a Princess Phone also has a thin body (the design) and a good tone (the ring-tone). In the second joke, Dorothy is using "institution" in two ways: (1) People sometimes donate large amounts of money to institutions (like schools and hospitals) so that their name will live on after they die; and (2) "Institution" also can mean a mental hospital. So the joke is a good double-entendre (using a word for two different meanings).

The first quote is just Dorothy teasing Blanche. The second quote Dorothy is saying that the only place Blanche could actually believe she'll live forever is inside of a mental institution