1. Probability Density Function

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2. You have the joint density of Y1 and Y2.
Let W=Y1 and find the joint density of W and U.
(That's calc3, jacobians.)
Then integrate out the unnecessary rv W.
And start showing your work here.

The other one is calc1

$\displaystyle f_U(u)=f_Y(y)\biggl|{dy\over du}\biggr|$

3. Not quite sure what you are talking about.

4. You should review calc3, change of variables.
Look at jacobians and the examples of polar, cylindrical and spherical coordinates