could be as simple as rock or something on the rotor but it is almost shorley the brake pads are worn out.

Several possibilities; warped front brake rotors, worn / faulty wheel bearings, loose brake caliper mounting bolts.

It depends on the type and frequency of the pulsing. Typically, the ABS system - when functioning properly - applies hydraulic brake pressure hundreds of times per second - what you'll feel is a heavy 'humming' at the brake pedal.

Need more information - what is meant by..'they go out...'? Does this mean you have low pedal, no pedal pressure? Does this mean loss of brake fluid when the pedal is pressed? If there is a loss of brake fluid, then inspect the brake system for external leaks - check both the rigid line (tubing) as well as the flexible brake hoses at the brake calipers. Also, check the brake master cylinder for leaks.
Finally, and once the leaking components are replaced, be sure to properly bleed the brakes. Use the 'How-To-Guides' feature on the AutoMD website for the specific steps.
Check on-line for the many parts supply sources, such as; www.autopartswarehouse.com or www.rockauto.com for the replacement parts.

Try the 'How-To-Guides' feature on the AutoMD website for the general repair steps. You can also reference the auto shop manuals at your local library.

Not necessarily common for the master cylinder at 52k miles - but still possible. Parts life (longetivty) somewhat depends on the maintenance provided - for example, in the case of the brake system - when was the last time the old brake fluid in the system was changed / flushed and replaced with new fluid - according to service recommendations?

Try the many on-line auto parts sources, such as; www.autopartswarehouse.com or www.rockauto.com for the replacement parts.

Check the 'How-To-Guides' feature on the AutoMD website for the specific steps to bleed the brake system.

No. why did it need a booster?