I've discovered Bitcoin few days ago, but I am skeptical about few things, why would I invest money in Bitcoins at the end of the day,why would I convert money into Bitcoins?
To escape from the traditional banking system.
If I want to buy stocks or invest money I can easily invest with real $. Why would I convert my $ to bitcoins?
See above
If I want to gamble , I can simply gamble on websites that require $ as currency, why would I convert it to bitcoins?
Not sure here, but maybe Bitcoin because Bitcoin deposits are faster.
What's the difference between Bitcoins and dolars? What does bitcoin bring to the table that real $ don't, less taxes, more income?
Taxes depend on your country. You don't get more or less income with Bitcoin. You get freedom, faster transactions and a way to keep your money yourself, safely.