Stanford - Menlo Park public transportation (?)

It really depends on where in Menlo Park they will be living and where on campus they will be going. Much of Menlo Park borders (literally) the Stanford campus. But the campus is huge(8000 acres, IIRC), so it also depends where they're going (for example, the hospital is quite near Menlo Park, but some of the graduate housing on campus is definitely not). Bicycle is the preferred form of transportation on campus (as well as roller blades and skateboards)and certainly, if they don't live too too far from campus, then from home, too. Public transportation is not great -- there are buses, but it would probably take longer to get to the bus stop than to get to campus. If they do decide on bikes, "junkers" is the way to go -- nobody uses really good bikes -- too much chance of them getting stolen.

Generally yes.
Lots of people bike, there is a free shuttle (margueritte) which serves Stanford area and there are local buses. But without knowing where in menlo park you will be staying it is j
hard to say. We live in Palo ALto right near Stanford and hardly go anywhere except by bike.
I'd suggest getting on the International Center webpage at Stanford that has lots of good information

Biking is an option.

There's bus 22 that runs along El Camino Real (a major street in that area):

http://www.vta.org/schedules/SC_22.html

The Marguerite shuttle runs within the campus and connects the campus to public transportation:

http://transportation.stanford.edu/marguerite/MargueriteSched.shtml

The KX bus connects Palo Alto to SFO airport and to San Francisco:

http://www.samtrans.org/schedules.html

For San Francisco, you can also take the CalTrain.

Another thing you can try: Go to maps.google.com and type in "from Stanford University to Google" and toggle to "By public transit." You can get a list of potential buses this way (and you can then Google for the bus route you need).

And obviously check Stanford's website, which should have further transportation details.