Rattling Noise from the Front Passenger Wheel?

The noise is only heard when my foot is not on the brake, which means I can hear it during acceleration. The noise goes away and comes back daily. It's annoying me that I sometimes lightly tap or lightly hold the brake pedal to make the noise go away. Anyone know the solution to this? Its a Honda Accord 2006. I'm thinking that the problem could be the brake shims or brake clips. There's no problem when braking, no noise, or any shaking on the steering wheel. I'm certain that the pads or rotors are not the problem.

Does my car have Lifetime water pump?

According to the owner's manual, it says to *check* the water pump at 105k miles but doesn't say anything about replacing it.

So does this mean mine is good for life? I have a Honda.

Can 1996 Honda Accord run okay without catalytic converter?

Someone cut mine out and stole it. Assuming it is legal to do so, can I straight-pipe to the muffler? Will the car run correctly? I'm hesitant to put another cat-converter and have it stolen again.

Added (1). Obviously it is illegal to remove a cat-converter. Legally driving without one depends on where you live.