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?

Normally anything under a year is a bit suspect, a year is not too bad, 18 months to 2 years is fine. A lot depends on whether there is a trend.

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)?

Just be honest without making any personal remarks about managers. "The job wasn't really a good fit. I'm looking for work which suits me and will advance my career."

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?)

You can't make sure, but normally they will not contact your old job because they know you're still working there. It's a risk you need to take if you apply for jobs while still working elsewhere.

In big cities it doesn't normally happen, but I can tell you by experience that in small communities, and small industries, it actually does happen. I had an interview once and as soon as the receptionist saw me (not even the interviewer) she was on the phone to a friend of hers at my work. (I still got the job, and had her fired, but it caused me quite a bit of grief with my old company).

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?

Normally anything under a year is a bit suspect, a year is not too bad, 18 months to 2 years is fine. A lot depends on whether there is a trend.

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)?

Just be honest without making any personal remarks about managers. "The job wasn't really a good fit. I'm looking for work which suits me and will advance my career."

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?)

You can't make sure, but normally they will not contact your old job because they know you're still working there. It's a risk you need to take if you apply for jobs while still working elsewhere.

In big cities it doesn't normally happen, but I can tell you by experience that in small communities, and small industries, it actually does happen. I had an interview once and as soon as the receptionist saw me (not even the interviewer) she was on the phone to a friend of hers at my work. (I still got the job, and had her fired, but it caused me quite a bit of grief with my old company).

Since you're in your trial period then you can quit anytime without it making a big difference in interviews. You just say the job was a bad fit for you. It's what trial periods are for, to test fit.