1. How long after starting a job is it ok to change it? Should I wait few months more even if I know I will never be happy in this company?

As has been said, anything under a year is suspect unless it was a contract. That said, quitting a bad position is better than being fired.

2. For sure if I get a new interview from a new company the first question will be why I am quitting a job after such a short time. How should I answer and justify this (if it helps, I was 6 years in my previous job)?

As Joe Stazzere said, be honest. We've all had jobs where we just didn't fit in. You don't have to deride the company or management. Saying it wasn't a good fit is the most professional approach. If pressed, you can say that your previous employer's management style was incompatible with your working habits. This gives you the opportunity to then expound on the wonderful management style of your prospective employer. Always turn a negative into a positive. As an aside, always research the company you are applying to so that you can expound on their virtues

3. How to make sure that the company I apply for will not contact my current employer before offering me a position? (do they do that?)

If you are presently working for someone, a prospective employer will almost never contact your current employer. There is too much liability involved. If they contact your employer and you get fired, they can get sued. However, if you quit before getting a new job, they can and will contact your present employer. The old rule of "don't quit a job until you have a new one" applies in spades in this case.

Also, don't be too concerned since you have six years at one job prior to this one. Anyone can make a bad move, but since you have six years of continuous employment at one employer, that will bolster your stance that this was just a bad fit. "Yes, I left that employer after four months, but I was at my previous employer for six years. It was just a bad fit, and rather than waste their time and mine, I decided to move on"

1. How long after starting a job is it ok to change it? Should I wait few months more even if I know I will never be happy in this company?

As has been said, anything under a year is suspect unless it was a contract. That said, leaving a bad position to go to a better job is better than being fired.

2. For sure if I get a new interview from a new company the first question will be why I am quitting a job after such a short time. How should I answer and justify this (if it helps, I was 6 years in my previous job)?

As Joe Stazzere said, be honest. We've all had jobs where we just didn't fit in. You don't have to deride the company or management. Saying it wasn't a good fit is the most professional approach. If pressed, you can say that your previous employer's management style was incompatible with your working habits. This gives you the opportunity to then expound on the wonderful management style of your prospective employer. Always turn a negative into a positive. As an aside, always research the company you are applying to so that you can expound on their virtues

3. How to make sure that the company I apply for will not contact my current employer before offering me a position? (do they do that?)

If you are presently working for someone, a prospective employer will almost never contact your current employer. There is too much liability involved. If they contact your employer and you get fired, they can get sued. However, if you quit before getting a new job, they can and will contact your present employer. The old rule of "don't quit a job until you have a new one" applies in spades in this case.

Also, don't be too concerned since you have six years at one job prior to this one. Anyone can make a bad move, but since you have six years of continuous employment at one employer, that will bolster your stance that this was just a bad fit. As HGLEM said below, you can address this with your prospective employer: "Yes, I left that employer after four months, but I was at my previous employer for six years. It was just a bad fit, and rather than waste their time and mine, I decided to move on". As HGLEM said, this will show that you will stay if it's a good fit and leave if it's a bad fit and can open up a dialogue on just what makes a good or bad fit for you. This is useful for all parties concerned because as you've learned, a good fit is important for both you and the company. Interviewing is a two way street. Use this experience as an opportunity to ask better questions in your next interview so you know what kind of environment you will be joining and whether or not it will be a good fit.