There's 2 things in your question: the cause of the trouble and the cost of the repair.
For the cause of the trouble, a defective alternator or battery are unlikely to be causing the ABS light to come on, your instruments to turn off and the radio volume to change. The most likely cause of all this would be the ECU (Engine Control Unit, sometimes called the PCM, the Powertrain Control Module), or some bad electrical wires (they wouldn't be loose, they would be corroded, or have the insulator cracked).
Have your mechanic friend inspect all your wiring:
- the wiring under the hood
- the wiring in the central console
- the wiring behind your instrument cluster
- the wiring near your ECU and ABS controller
You may want to try a replacing your ECU by a used one from the junkyard. Some junkyards have the components sitting on a shelf, some junkyards have you going out to the car and removing whatever components you need. I personally trust these do-it-yourself junkyards more, because I can know for sure WHICH make and model the component came from.
Whichever junkyard you get the component from, your mechanic friend can swap it easily. If it resolves your issue, then you can choose between using the junkyard ECU or looking into whether your old ECU is still under warranty (ECU's often have an extended separate warranty longer than the car's, mandated by the government).
If you still suspect the alternator and battery, get a multi-meter ($15-$20 at WalMart) and do the following test (no tools or expertise are required, so you can do this yourself):
- With the engine off, open the hood and prop-it up securely
- Make sure your leads (your 2 wires) are connected in the appropriate ports (do not use the "10 Amp" port for this test, use the common port. Your multimeter should have instructions on which port to use for a voltage test)
- Turn your multi-meter to "20 VDC"
- Find your battery and touch the metal part of your red wire to the battery connector marked "+" (it often has some red plastic near it) and touch your black wire to the battery connector labelled "-" (it often has black plastic near it)
- While each of your wires is touching it's battery connector, read the number on the screen. 12.6 or higher is a healthy battery that is fully charged.
- Put your multimeter down someplace away from metal, make sure the leads aren't touching anything and go start the car.
- Repeat this test with the engine running, now a voltage reading of about 14.0 is for a healthy alternator that is providing a full-charge.
- Put your multimeter down safely and go into the car and turn everything electrical on: the rear defrost, the headlights and the heater fan.
- Go back and redo your voltage test (still with the engine on), a voltage reading of 13.0 or higher indicates your alternator is still supplying a full charge while under heavy load.
For more details about this test, see here.
As for the cost of the repair, we're not really supposed to comment on that here, but going to a mechanic shop or the dealership will always balloon your repair bill: they are not only charging you for the parts, they are charging you for the labour too. In my experience, the cost of the parts is usually between 1/3 to 1/2 of the total bill, the rest is labour. Find an auto parts store near you, give them your make and model and they will tell you how much an alternator and battery cost, then ask your mechanic friend how much he wants for installing these for you. As you said, these are simple repairs.