TL;DR; There is no silver bullet. You have to decide how much to invest and when on your own.
Averaging down definition:
DEFINITION of 'Average Down'
The process of buying additional shares in a company at lower prices than you originally purchased. This brings the average price you've paid for all your shares down.
BREAKING DOWN 'Average Down'
Sometimes this is a good strategy, other times it's better to sell off a beaten down stock rather than buying more shares.
So let us tackle your questions:
At what percentage drop of the stock price should I buy more shares. (Ex: should I wait for the price to fall by 5% or 10% to buy more.)
It depends on the behaviour of the security and the issuer. Is it near its historical minimum? How healthy is the issuer? There is no set percentage. You can maximize your gains or your losses if the security does not rebound.
The strategy is often favored by investors who have a long-term investment horizon and a contrarian approach to investing. A contrarian approach refers to a style of investing that is against, or contrary, to the prevailing investment trend.
On the other side of the coin are the investors and traders who generally have shorter-term investment horizons and view a stock decline as a portent of things to come. These investors are also likely to espouse trading in the direction of the prevailing trend, rather than against it. They may view buying into a stock decline as akin to trying to "catch a falling knife."
Your second question:
How many additional shares should I buy. (Ex: Initially I bought 10 shares, should I buy 5,10 or 20.)
That depends on your portfolio allocation before and after averaging down and your investor profile (risk apettite).
Take care when putting more money on a falling security, if your portfolio allocation shifts too much. That may expose you to risks you shouldn't be taking. You are assuming a risk for example, if the market bears down like 2008:
Averaging down or doubling up works well when the stock eventually rebounds because it has the effect of magnifying gains, but if the stock continues to decline, losses are also magnified. In such cases, the investor may rue the decision to average down rather than either exiting the position or failing to add to the initial holding.
One of the pitfalls of averaging down is when the security does not rebound, and you become too attached to be able to cut your losses and move on.
Also if you are bullish on a position, be careful not to slip the I down and add a T on said position. Invest with your head, not your heart.