Under capitalism, these questions are meaningless.
The fallacies of intellectual communism, a compilation - On the nature of power
None of these questions are taboo and all of them have pretty simple answers. The problem is in the way that you frame the questions. They are all leading questions that include the underlying assumption that communism (or socialism, they're both the same thing) is the only desireable economic system.
Julio: How much Income inequality is apropiate for a healthy Capitalistic system???
There is no limit to the appropriate level of income inequality. Everyone receives whatever income they can manage to get for whatever goods or services they choose to provide. Ultimately, the only answer to this question is that the market will decide. I think that's it's inappropriate for you to ask a question and exclude the only correct answer.
Julio: How much does it take to have competitive industries ???
The only thing that is required in order to have competitive industries is to remove government regulations and eliminate taxation. People in business are naturally competitive and there is nothing that the government can do to make them more so. Any regulations only stifle competition. There's a book called The House of Morgan that describes how both J.P. Senior and Junior managed to do this in building their empire. Yes, the Morgans were socialists.
Julio: What is the appropriate employer/employee relationship???
This relationship is strictly voluntary. The employer can hire whoever is willing to work for him/her at whatever wage and benefit combination they are willing to accept and the employee can work for whoever is willing to hire him/her for the wage and benefit combination that he/she demands.
Julio: How much Education and Health care should be provided by the Govt???
The same amount that you would provide the a random person who happens to sit next to you on a train, which is to say, none. Education and healthcare are so messed up precisely because they are provided by the government. Web-based retailers such as Amazon work so well precisely because they are subject to much less government regulation.
I hope that these answers inspire you to learn a little more about economics. It would be great if you could ask some questions that actually required some thought to answer.
Julio:How much Income inequality is apropiate for a healthy Capitalistic system???
However much market actors want.
Julio:How much does it take to have competitive industries ???
I don't understand. Are you asking "what does it take to have competition?" ? If that's the case, varying wants and varying suply to those wants.
Julio:What is the appropriate employer/employee relationship???
A relationship the employer and employee agree to.
Julio:How much Education and Health care should be provided by the Govt???
Begs the question, should the government be a provider? No.