For the first question; any object moving in a circle, regardless of the reason why it is moving in a circle, feels a resultant force that we call the centripetal force, for which there is an equation that I am sure that you know. Now, put that aside and just think what the forces acting on an object at the surface of the Earth are. Weight going towards the centre of the Earth, of course - anything else? Once you've got the resultant of the "regular" forces worked out. put it equal to the centripetal force - after all, the resultant of these forces is what we mean by the centripetal force. Finally - that "other" force from earlier - what happens to it when the Earth is spinning so fast that objects are about to be flung off? If you can see that, your equation should simplify a bit, and although there is still a little work to do, you're nearly there.
For the second question; do you know an equation for the gravitational field strength at a distance r from the centre of mass of an object of mass M? If so, work out g for both stars (in terms of y and d), and put them equal to each other (because if an object feels the same pull of gravity from both stars, but in opposite directions, it will feel a zero resultant pull). This won't enable you to find y or d, but it will let you find y/d.