You're in good hands with Chicklet teeth (), you definitely have a charging system issue. Maybe it's causing the stutter too? Once you do all his wiring/connector checks, you can start checking the system components. If you have a DVOM, they are listed step-by-step in the manual and easy to do.
I would 98% bet you have a voltage regulator going bad. Besides the wiring Barrett told you to check it's about the only cause of an intermittant charging issue. Not super common in an XB so a stock replacement is an easy swap, but there are upgrades you can do if you're feeling sassy.