Whenever I push the break down and press the power button (putting it into READY mode), yellow warning lights show up on the dashboard (such as ABS, brake, etc.) for about a second or two, then disappear when the car is ready to drive. I went to a mechanic and they told me that this is normal, and that I should only worry if those lights stay on and don't turn off. I just wanted to know from fellow Prius drivers if the mechanic's statement was correct and that this is normal and that I indeed should not worry. - Also, they 12v battery was tested and it came out as 12.5v
The warning light come in briefly to confirm for you that they are working, and not burnt out. You should be concerned if you don't see them in startup.
You appear to be new to owning a Prius. Do yourself a favor and read the owners manual in its entirety. If the manuals are missing, you can download it from Toyota.com, Owner section, as a PDF. Get into the habit of checking the oil level on a regular basis as well.
Replacing the battery just because is a hugh waste of resources. Replace it if it fails testing, otherwise, leave well alone.