Unless you are a master plumber or have experience doing this I would definitely get a plumber. I took a class over at Home Depot to switch out my pipes. At the store it seemed so simple and I got it right at the store. However when I got home it was a total disaster. Always get an expert
No you do not need a plumber to install a under-mount sink. Many come with instrctions that anyone can do. Most are self explanitory and are very easy to install
Your town or county's building codes might require a plumber to run any new water line and sewer line, so officially maybe. Check with the local building inspector. If they say it is OK, then, yes, you can do it if you do a little research and don't mind getting dirty and messy.