Constant high pitched whining noise. Increases

Could be one of the belts slipping or worn out. Might even be the water pump bearing. Does the whine increase/decrease as you rev? Whine louder if you suddenly accelerate?

Check your power steering fluid level ?

The fuel pressure regulator & spyder assy, most likely is bad

Don't think that is your noise though

Check trans fluid,may be pump noise

check the belt tensioner.

The noise you're hearing is the electric fuel pump in your fuel tank.

This could be anything from the pump in the transmission to the alternator bearings/bushings to the power steering pump. Could be an idler pulley bearing, but I doubt it.
Hint: If the noise is very high-pitched, check the alternator. If it is a lower, medium-high-pitch sound that changes some when you turn the wheels, check the power steering pump. If it is almost like a moan or a "Whooo" sound, that's the transmission pump.

hey not sure if its totally right but the high pitch squeal at when its idleing could be the tentioner pulley bearings on the engine belt not sure about the whining noise when its shut off

it is your idler pulley. get it from dealer comes with bracket, just use pulley off bracket. take your belt off and your idler pulley is lower right hand side(facing your engine). 15mm bolt, replace pulley and reinstall your belt. it;s a common problem on trailblazers

You didnt indicate whether you ran the engine with the belt removed while replacing the alternator,if not do so and verify noise. Sounds like you may have a vacuum leak, best way to diagnose would be with a smoke machine if not available with the engine cold try spraying carb cleaner around the intake & any suspect vacuum hoses with engine idling look for a change in idle speed or elimination of noise. Hope this helps you out

Alternator?
Voltage Regulator?

If the noise sounds like a weeeeeee that increases in pitch as the RPMs increase, and you haven't heard this sound before the 'problem', suspect the alternator...