私はアメリカ人です。二十二才の学生とベジタリアンです。
The の in simplest terms is a possessive particle and in this case it identifies that you are a 22 year old student.
The closest particle to "and" is と
You are correct that 私 is typically only needed at the beginning since you normal use は which identifies the topic. Normally you would only use it again if you were using it to contrast something they were talking about.
August 20, 2014 at 3:55pm