How does Sharpe Ratio work and what are the disadvantages of using it?

All the Sharpe Ratio measures is how much excess return (meaning return above a "risk-free" investment like US Treasury Bonds) you get for each "unit" of risk. In this case a unit is 1 standard deviation. So portfolios with a higher sharpe ratio use risk more effectively.

Why I am getting a different value other than Yahoo Finance?

Most likely because you're calculating return differently. The return in the sharpe ratio calculation is the return of the portfolio over that period over a risk-free return (in reality you can use 0 as a "benchmark" risk-free return, but most likely Yahoo is using a risk-free rate of some sort). So you would take the geometric average of returns (not arithmetic) and subtract a "risk-free" rate at the end. There are multiple articles in the internet on how to calculate Sharpe Ratio.

As I understood the higher Sharpe Ratio, the better. Why do not investors just calculate Sharpe Ratio for all stocks and invest in stocks with the highest stocks?

This is only true when comparing investments of similar risk. A bond portfolio may have a much higher sharpe ratio than a small-cap equity portfolio because it has much lower risk. For example, a bond portfolio that has an excess return of 4% with a risk of 2% would have a sharpe ratio of 2, while a small-cap equity portfolio may have an excess return of 10% but a risk of 8%, for a sharpe ratio of 1.25. So if you are a risk-averse investor, the bond portfolio may be a better use of risk, but a risky investor may want the portfolio with a higher absolute expected return (i.e. willing to risk more for the possibility of earning more).