M6600 CMOS battery. Rechargeable or not? How to confirm?

I want to first mention some symptoms.  Some are likely battery related, some maybe not.  

1.  Time randomly jumps around.  Sometimes tracks right for an hour, then changes by hours.  

2.  Machine will not boot correctly with AC adapter present.  If I remove, it will boot fine, then plug AC back in, all is good.  AC power meter shows max 40W if trying to boot with adapter plugged in.  Boot fails.  If allow to boot with battery, then AC adapter pulls up to 160W.  

3.  Wifi loses connection constantly.  3-4x/hr.  Reconnect and all is good.  

4.  Loss of display (black screen) randomly but rare.  Can still hear Windows running.  Reboot and it works again.  

5.  Full charge battery will randomly just show 0% and shut machine down.  With AC present, it still does that.  100%, then pops to 0% for about 10sec, then back to 100%

BIOS

A12, Optimus turned off, Events are low batt from years ago, nothing recent, fan malf recent.  Thermal events 3x fan1 stopped recent.  Date is correct but clock seems stopped from when power was removed.  Seconds do not change.  AC adapter IDs as a 240W, which is correct.  

On the battery, per "AI", the battery is rechargeable, others are saying it isn't!  I cannot confirm the PN on the battery, already looked.  

Would this erratic behavior be caused by the battery?