94 Regal, ABS, ground issue?

[7rish13]

1994 Buick Gran Regal, 2 door, 90,000 miles, all power.
I've only owned this car since late last summer, from first owner.
Everything on it worked, except it needed a new caliper on the rear wheel. Changed caliper.
Didn't notice until recently, that each morning I'd start the car, turn on parking lights, pull out, once in alley I'd then turn on the headlights.
About 20 feet or so there'd be a noise from the ABS, as if engaging, then quickly my lights would flicker. Most of the time my ABS light would stay on, or not come on until I needed to brake quickly.

Now, just recently the E-brake light would come on and stay on. To where I would engage and disengage the E brake, light would remain on. MOST times the E-brake light wouldn't even come on. I've never needed/used the E-brake, except to engage/disengage to get light to go off. Didn't work, light came on it stayed on. Until I started the car again next use.

Over a recent cold snap, my battery died, so i jumped it. the guage suggested low charge, replaced battery. Still low charge on battery, replace alternator.

Car worked and ran fine for about a month, then the ABS light came on and I was back to flickering lights when turned on. Gauge read "low battery" and/or would even move up and down.
Can't risk taking to/from work. Sitting in my driveway now, until I can fix this.

I'm at a stand still. Any helpful suggestions would help.

Thank you,
And if this is posted in the wrong selection, my apologies.
T~>