A bit late to answer, but your issue looks like the dry solder issue iBook G4 was plagued with. And yes it can be fixed: https://macintoshhowto.com/hardware/how-do-i-get-my-broken-g4-ibook-fixed.html
The Macintosh Portable is the easiest to open and access it's internal parts. On the desktop line, some modeles like the PowerMac 7500 is really easy to open too.
Yes it should. When I went to an apple store to replace my battery that started to inflate, they asked if I wanted to juste completely remove it or get it replaced.
But don’t forget that without the battery, once you unplug the laptop it is like removing the plug of a desktop computer: everything goes off instantly.