Question:  Do I need to know how to type to make it through law school?
Answer:    Even in this computer age there are people who get through law school utilizing only handwritten materials.  But their numbers continue to drop.  You should make learning to type a priority for several reasons. 
    First, even the best handwritten materials are harder to read than typed words.  Also, by learning only basic typing skills you will be able to type much faster than you can write, and you'll be able to read it!  Third, as you begin performing legal research, the electronic databases all require keyboarding skills.  And last, while there will only be a moderate number of assignments that need to be handed in during law school, no prof will accept handwritten materials.  In that case, you would be forced to hire a typist and act as editor after already having written out the material.  Twice the work is twice the time; time you won't have.
    So the direct answer to your question would be a qualified "yes".  Personal computers, word processing and the Internet have made the world keyboard oriented.  It's time you faced the fact that you need to make an adjustment and learn to type.
Question:  Is owning a computer a necessity?
Answer:    You can use the computers at the university computer lab.  But that will not be a reliable source if there are not enough to go around, and you find yourself waiting in line.  If you choose that path, you will be dealing with network printer problems, carrying disks around, etc.
    Computers have come down in price to the point that it would be hard to justify not owning your own.
Question:  Is owning a laptop computer a necessity?
Answer:    This is an easy "no".  You will see many laptops at law school.  No doubt they can be handy.  However, they remain very expensive, and that cost is not outweighed by the benefit.  Taking handwritten notes in class will prove sufficient.
Question:  Does any one undergrad major have an advantage?
Answer:  While I've never seen any statistics pertaining to the question, it's widely viewed that no single major enjoys a benefit over another.  It was thought for some time that Political Science majors enjoyed an advantage due to the fact that they had already read cases prior to attending law school, but having read cases is only a fraction of what is required to be successful at law school.
Question:  Can you recommend some general legal sites that might prove helpful to the pre-law individual?
Answer:  Absolutely.  I believe that www.findlaw.com and www.hg.org (Hieros Gamos) are two of the finest and most helpful sites you are going to find.  Both are used heavily by the legal community at large.  Also, both have sections devoted to law students and those considering attending law school.