Where necessary it looks like formulas are "built into" the questions. There's no special formula sheet supplied.
For quadrature, look at p304, long enough to realise that it's essentially the same thing as you were doing with two variables. I my haste and desperation last year, this fact just sailed right over my head.
As you say, there are two things you need: w, and t.
t, you get from the Legendre polynomials (or the roots thereof). For 2-term the solution of the equation is easy. If you have difficulty you're just making some simple mistake, so rewind a bit till you find it instead of improving your cursing skills.
Once you have your t, you can solve the system for w.
For three terms you have 3 w.
For a three term quadrature your POLYNOMIAL is exact up to degree 2*3-1 = 5. 5 degrees plus the zero power term = 6 equations.
In some of the papers they've asked for a general outline of how you would solve for the missing parameters, and you've now reached the end of a rough version of what my summary would look like since I became a sadder but wiser man. (Or since the dismay of last year's failure if you don't like poetic allusions).