1999 Chevy S-10 low amperage reading on gauge, warning ligh

YES.
It could be any or all of the above.
The only way to tell for sure is to test them and find out. You can test the battery by hooking a voltmeter (which is what is in the dash NOT an ammeter) onto the battery with the negative lead off. It should read over 12-12.5 volts with no load. Any lower and it is either undercharged or has a bad cell. Being that you have a problem it will read low, you need to put a charger on it to bring it up so you can test it.

For the alternator you will need to take it to a shop, either the alternator itself OR take the vehicle in. The regulator is split in that vehicle, some of the parts are in the alternator itself and the rest are in the ECM (computer) itself.
Many of the parts stores will test the alternator free if you take it in.