Hi there bijumac,
For the issues with the cursor and battery life on your Mac, we'd suggest running Apple Diagnostics to check for any hardware-related issues. Start with these steps:
Prepare your Mac
1. Shut down your Mac.
2. Disconnect all external devices except keyboard, mouse, display, Ethernet connection (if applicable), and connection to AC power.
3. Make sure that your Mac is on a hard, flat, stable surface with good ventilation.
Then, dependent upon whether you have Apple silicon or Intel processor on your Mac, follow the remaining relevant steps here: Use Apple Diagnostics to test your Mac - Apple Support
If you don't see any hardware issues, you can maximize battery life with these suggestions: Get help with your Mac laptop battery - Apple Support
Let us know how it goes.
Cheers!