Macbook Air Crashing Due to Old Battery?

I wouldn't expect the battery to cause system freezes or crashes under most circumstances. A bad battery could potentially cause the system to run slow.

Run the Apple Diagnostics to see if there are any other hardware issues.

Try running the laptop in Safe Mode to see if you have the same issues. The screen may flicker or flash due to the very basic video driver being used. This will disable most startup & login items.

Run EtreCheck and post the report here using the "Additional Text" icon which looks like a piece of paper.

Uninstall CleanMyMac by following the developer's instructions. Cleaning apps are not needed on a Mac and they cause more problems than they solve plus they impact system performance.

Be sure to keep at least one or two backups; in addition to Time Machine, on external

USB drive. Also try backup clones, gives you practice with ideas not generally done.

Since repair service can only keep track of troubleshooting & repair; keep spare backups!

An authorized Apple service shop, could be used to troubleshoot & repair MacBook.

• Apple Repair and Repair Status Check - Official Apple Support

https://support.apple.com/repair

{..Some regional authorized service centers are able to accept "mail-in" service repairs.

This would have them sent you a box, you'd return mac for inspection/repair inside..}

Good luck & happy trails!🌻☘