When players are waived and signed by another team how much of the player's salary and bonus' is the original team responsible for? How much is the new team responsible for?

The new team is only responsible for the base salary (salary minus the bonus) if they get the player in a trade. When a player is waived their old contract is destroyed, they get the remainder of their bonus and when they sign with a new team they get a whole new contract.

None of their salary is guaranteed. The only guarantee is signing bonus and that is why players are more concerned with signing bonus' money vs salary. Teams can cut a player at anytime and not have to pay his salary.

Now the salary cap is another story altogether.