So many questions... Yes, every rotating thing has a life span. The faster it rotates, the sooner the total is reached. Don't fear, though, the rotations are counted in many tens of thousands of hours, meaning several years of use. However, that can be reduced by dirt, gunk, heat... Should you ever have to clean a smoker's computer, you'd move your ashtray outside!
Since you haven't had any third party software for controlling the fans before changing the battery, it has been done in the BIOS. Taking the old battery out has reset the settings to safe defaults. You might want to try the "optimized default settings" or something like that, it's usually on the last tab with the save and quit options. If that doesn't do the trick, dig deeper. Look for "smart fan control" and such, enable them, set the thresholds a little higher if you dare or lower the percentages at certain temperature levels. Bear in mind, though, that you'd rather let the fans blow a little louder than let your computer fry to death! If the fan noise annoys you, get more and bigger fans. Seriously, that's the recipe for a cool and silent computer: More and bigger.
[edit] I would have loved to provide a 101 on the subject, but each motherboard has different settings. Scroll through all of the (advanced) settings and check each one even vaguely related to fan speed. If the description is inadequate, Google is your friend. You know it's doable since you've noticed a difference.
