In this story line, a Red Stone does indeed have the power to bypass the natural laws of alchemy such as1:
- The requirement for transmutation circles
- The Law of Equivalent Exchange
- The required alchemical knowledge to perform alchemy
The goal of alchemists was to find a way around the known laws of alchemy, which is why they had the goal of creating the Philosopher's Stone in the first place. Red Stones are a result of their efforts at such research and thus have similar capabilities as a true Philosopher's Stone. However, while they do not require human sacrifice, they are not as powerful and can cause adverse effects to the user in the form of rebound. An example of these rebounds is the effect on Cornello's arm when the Red Stone crumbled.
As far as your question about the birds, there has been a similar question already asked here on stack exchange.
It's important to note that the information I've provided is only relevant to the 2003 production. In the original manga, Red Stone is simply another name for a Philosopher's Stone, and the stone Cornello used crumbled because it had run out of souls. Ed believed it to be a fake because he was still under the impression that the Philosopher's Stone was a source of unlimited power1.