On regular GB games the life span for a battery is in the decades, for gb games with an RTC I think you can expect ~8 years, with the ezjr using a smaller battery it's hard to say, but it should last a few years.
In regards to the saves: the flash card saves progress onto the battery powered SRAM initially but writes those saves to the SD card on the next boot or reset (pressing the button in the cartridge). So those save games are safe. If you always reset before powering off the console, you won't even need to change the battery, allthough the RTC will stop working.
Allthough you will lose progress you made in game when you power off the system without a reset.