Answer to question #1 is yes. A witness may be compelled to testify despite a Fifth Amendment invocation if it is court ordered, which is rare, and happens in administrative, governmental hearings. If a witness testifies to a certain matter, and then seeks the protection of the Fifth, she may still be cross-examined within the strict boundaries of her former testimony.

However, under Kastigar (I forget the year), compelled testimony may not be used in a subsequent proceeding/trial over the defendant's guilt. And the prosecution in the subsequent trial has an onerous burden of establishing before the court that the evidence is entirely from evidence, independent from the compelled testimony in the former proceeding. This is the basis, on which Ollie North's criminal conviction was overturned: the prosecution could not meet its burden on appeal proving that the evidence against him did not result directly or indirectly from the former compelled testimony.

The Fifth's privilege does not extend to physical evidence, such as papers, emails, personal effects, etc. as those are determined by the Fourth and Fourteenth. Similarly, a person can not seek Fifth Amendment protection from the results of a blood test.