99 Ford Escort: At start-up, the area that hold the timing belt makes a loud rocking noise, then goes away?

If it is not the belt cover rattling get it done quick. Escorts are notorious for terminal belt failures even before the due replacement date. Most should have it done at least every 40,000 I seem to remember.

Old mechanic.

The oil in the sump is sucked into the oil pump, the oil pump forces the oil into the engine. the first position the oil is going is the significant bearings of the engine, after the mains the oil then travels round something of the engine. In different words the significant bearings produce the oil stress interior the same way that water in a hose pipe may be pressurized once you positioned your finger over the end of the pipe. From the sound of what you've said i think that the significant bearings on your engine are damaged ensuing in both the noise and the oil stress caution gentle coming near. regrettably you'll choose both an finished engine re-construct or a re-conditioned change engine. Ja.

It's a danger, broken belt could badly damage your engine.

Yes, have Ford replace the belt. 95k is change time, or maybe past change time.

If Ford's close, I would have it towed.

If Ford did the oil change, they prob would have noticed the prob.

Always have Ford do the regular maint including oil/filter change.

Name-brand dealers like Ford, VW, etc, do an included multi point vehicle check w/ the oil change, checking belts, hoses, fluids, charging system, etc.

sounds like your timing is bad have it checked and fixed if needed