The fob must be gently pried apart, the electronics unit removed, the battery replaced, the electronics unit reinstalled, and the fob snapped back together. Your owner's manual should tell you how, if not ask your dealer.
Before you can fix it, you need to diagnose what the problem is. Have you checked fuses and relays? Do you have continuity in the high beam circuit on the switch? Is there power to the point where the wiring harness splits off to supply each high beam lamp? Have you checked the bulbs? There are several different reasons why your high beams could be malfunctioning... without narrowing down the cause, you'll just end up wasting money by throwing parts at it until you get it right (if you do at all).
There's been 5. All minor except accelerator/stuck throttle (2) different ones for this, search for more
No. Ford is a separate company from Mazda, owned by the Ford Motor Company, that currently only owns Lincoln and Mercury and previously owned Merkur. Mazda is only related to Ford by 45% of their vehicles, but they are not the same company. Mazda is also its own company.