In the absense of any contract - ie as long as you work for yourself, you don’t have to give anyone anything. The problem, however, is that if this is the case then you should have discussed this with the client before starting the job. To the client it may seem unfair of you to refuse this now, if they had the expectation that you would provide it and you provided no indication otherwise.
and what do they want anyway? I use Fireworks mostly with photoshop occasionally.
They probably want the source images that you used to create the design, complete with layers - including everything they would need to modify the design. They may see it as an insurance policy, so that if they need further modification to the design in the future and you are no longer in business or no longer an option for them, they can get someone else to do it.
If I don’t give it to them and they want changes in the future am I obligated to change a background or images? My business is only for single pages mostly.
No, you are not obliged to work for them in future - that would be slavery. You can always refuse to do work for someone.
In this situation, however, it sounds like you came to no understanding with them beforehand about what would be included, so they are probably assuming they’ll get everything, including your source images. Refusing to hand them over will conflict with what they expected from you, which may make them very unhappy. I doubt that they would want further business from you and they may even consider taking action against you.
If you had agreed with them about what you would provide in the first place, then that’s different. But with no agreement you kind of have to accept that what you expect and what your client expects may be different, and while you may or may not be within your rights to refuse to hand over some work, it may make enemies, simply because there was no clear agreement before the work was done.
Of course, if you are an employee, then the situation is different again, because then they own all your work anyway. But it sounds like you are not an employee.
Yes. This is quite a valid strategy. You just need to communicate with the client beforehand about what is included and what isn’t - the problem is when the client had no idea that the proofs/PSDs would not be included and they feel cheated.