Bought a new alternator due my old one FAILED the test. But, I still have the problem with my head lights flickering & stereo going off then on when I accelerate to go.

It is possible that you have a faulty alternator. You do get rare occasions where a faulty unit slips through the system and gets sold. Please read this all the way through as it give more than one way to check for where the problem could be.
How old is the battery? They are considered 'Old' once they are over 5 years old. If you know how to use a multimeter try this.
You'll need to check both the alternator and the battery. For the battery - With the engine OFF test the DC voltage of the battery. It should be somewhere between 12.6 and 13.2 volts. Anything lower than 10 volts and it could be a faulty battery. Even a fully charged battery can struggle to supply power if it is old or worn out.
For the alternator - Start the vehicle and retest the battery voltage. It should read somewhere between 13.7 and 14.7 volts. If it's noticeably lower (or higher) it is most likely the alternator.
If you don't have a multimeter you can try a basic test. Get a helper to stand in front of the vehicle. With the park brake On turn on your head lights THEN start the engine. Your helper is watching for a significant dimming in the headlights. The lights should dim as you crank the engine then brighten again. Next turn everything else on, including the stereo, A/C, courtesy light. This is to put the battery and alternator under heavy load. If the headlights dim noticeably It is possibly the alternator.
Most companies often have a guarantee or a warranty on the alternator so a replacement shouldn't cost you anything.

Loose wires to the headlights or fuse panel.

fit a new bosch genuine factory exchange alternator ,that will cure it ,your existing alternator is worn out commutator/brushes worn

Usually it is not a fuse link, but use a test light and check that you have current at the main terminal on the alternator. If you do the fuse links are fine, so next check your belt tension this is something that is overlooked often and is the cause of flickering alternator lights. Also check and make sure your cable ends are clean and tight. If all is fine that alternator or the voltage regulator in the alternator is going bad.

You should have your alternator checked. If it is going bad, it won't produce the necessary power to keep your battery charged and run options like stereo, AC or heat. You might be lucky and a mechanic can fix it, but if you let it get burnt out it is going to cost considerably more!
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either the belt is slipping or the alternator is losing juice at a lower rpm....i take it it was checked in park,or taken out and tested by a machine which spins fast?

You have probably been getting 'rebuilt' units which is not bad in itself but if the rebuilder received a batch of bad diodes they may have these failures until they are exhausted.
But, buddy, you ain't broke my record yet; a lousy Saturn (LAST GM I will own!) bought new, ate SIX (6) alternators in 57,600 miles. That wasn't the worst problem; it ate the auto tranny at 31,000 and dropped a rod cap at the above final mileage.    

hi your battery may have failed or your altinator is not charging to recharge the battery proporly

I have over 300k miles on my 2000 Venture. When the lights start flickering at low RPM's, the alternator or battery might be going bad. I would have it tested (for free) at the local AutoZone or Napa. The alternator SHOULD last 80-150,000+ miles. Its a real pain to change out on the Venture vans.

Sometimes I wonder if the van just doesn't create enough juice to run all of the accessories since even when batery and alternator are new they flicker once in a while when a component turns on.

I get zapped year round by my cars, even in high humidity. It is not harmful, but be careful at gas stations!

Sounds like you have a bad alternator. but first , check the battery connection o the positive side where the cables overlap eachother. they like to corrode in between the two cables and do just what your saying. but it really sounds like you need an alternator. have someone check the red wire on the back of the alternator and see if there is power there al the time- should be. if so replace the alternator, i have had many new or not vary old one fail. - good luck