Cusser
+1y
"You might look at the battery ground cable for internal corrosion or where it grounds to the block for corrosion there. If you have a meter, you can check for running voltage at the battery. It should be between 13.8 and 14.6 volts DC. If a cable goes bad it causes the alternator to work harder trying to charge the battery and that could be where your issue is coming from. "
Do that test. A digital multimeter with 0 - 20 volts DC scale is under $25 to free at Harbor Freight with a coupon.
Measure that voltage across the battery terminals with engine running; do NOT remove a battery cable while the engine is running (you have an alternator, not a generator). Autozone and O'Reilly can check that for charging if you drive there, and free.
Yes, the alternator keeps the battery at charge so it can spin the engine to start it, and to keep it at that state. Yes, a bad battery can affect things.
My '88 B2200 with 215K still has its original alternator; but I replaced the alternator in my '98 Frontier with a rebuilt (lifetime) one from O'Reilly about 5 years ago, and it has held up fine.