wondering if there is way to check the alternator without taking it out?

 

yes, it's easy.

start the engine and measure voltage on the battery. it should be about 14V (not lower 13.5, not higher than 15V). then turn on lowbeam, highbeam, blower, some other accesory, voltage shouldn't be changed much.

be sure that your battery is not discharged.

 

what do you mean not discharged

 

As in besure your battery is FULLY CHarged

 

how many volts should the alternator give out the 14.5 volts

 

before starting your car, loosen your terminal bolts. start your car then take off the terminals...

the car should stay running

 

that's not a very good idea to taking off terminals from battery, while car is running.

14.5 V is ok.

 

Taking the battery terminals off while the car is running is a good way to burn up some control modules. The battery acts as a buffer eliminating voltage spikes.