Why analysts' estimates may differ significantly from market prices and should I follow their recommendations?

The major way to predict stock prices is analyzing the fundamental value of the company, based on growth, earnings, dividends, etc. As an example, an analyst may conclude that a company should be worth 20 times it earnings. He may expect that the company will grow next year by 5% and increase the earning by 10% and increase the estimated value accordingly. This may look like an exact science by computing two digits after the comma but as you can see there are a lof of assumptions and by changing any of those parameters slightly one might end up with a completely different value:

• What is a good multiple of earnings?
  10? 20? 40? Should this be the same for all sectors or is this supposed to be different for Google and Home Depot?
• How much growth is realistic for how long?
• How much should future earnings be discounted?
  After all, it is not guaranteed that it will happen
• How to account for companies that do not pay dividends or operate at a loss?
• What about events nobody expects? What about inventions that fundamentally change a market?
  When I was young in the mid 2000s, Nokia was the dominant manufacturer for phones. A few years later the company was basically wiped out because the market had been completely disrupted by smartphones

Some people predict stock prices by analyzing trends in the charts and hoping that either current trends will continue or past trends will repeat themselves. This is an even less exact approach to predict prices.

Should I follow these advices?
As explained this is inherently imprecise, even if we assume a capable analyst giving their best effort. There is no thing such as guaranteed free money.

Your question has intrigued academic researchers for decades. Here what a survey paper finds:

• Analysts’ Forecasts are Optimistic
• Analysts’ Forecasts Are Superior to Time-Series Model Forecasts
• Analysts’ Forecasts are Inefficient [my comment - they overreact or underreact to information]
• Most Academic Research Ignores Analysts’ Multi-Tasking
• Analysts are Dominated by Conflicts of Interest
• Limited Evidence Exists Regarding What Analysts Do with Their Own Forecasts
• We Think We Know How Analysts Forecast
• Empiricists Have Traditionally Not Embraced Alternative Methodologies (but This is Changing)
• Academics May Be Focusing Too Much on the Least Important Activities
• Analyst Data are Indirectly Helpful to Other Work Examining the Functioning of Capital Markets