Are all undecidable/uncomputable problems reducible to the Halting problem?
No. As I recall a practical example can be made out of a function inequivalence statement. More abstractly, there is something called Turing-degree in undecidability and infinite levels of "hardness".  Each level has it's own Halting Problem strictly harder than those at every level lower.  Check out the first section of this Scott Aaronson lecture and what he calls a "Super Halting Problem".