What is good age to start learning programming? I am thinking of offering classes for people, maybe take 5 to 10 at the time. There would be 4 hours every Saturday, twice a month, for three months. So in total 6 such sessions. The language thought would be Javascript (and HTML, CSS). 

I was planning to offer it to adults and kids, and especially interesting would be for a parent and child to do it together. 

What do you think is a minimum age for which I should accept students, alone and with a parent?
Let me urge a bit of caution if you try to combine teaching of youngsters with their parents. Before you decide, you should look at the work of Piaget on the stages of development. Adults and teens from about 12 can learn abstractly, but those younger probably haven't yet developed the changes in the brain (including physical changes) that make that possible. Starting from around 7 kids can learn things like computing, but only very concretely. 

I bring this up so that you don't wind up with classes that serve no one very well and frustrate everyone. Some programming environments stress the concrete and are good for youngsters (Scratch, Logo, and other visual systems) but adults learn very differently. 

If your goal is primarily to have the parents help their younger kids to learn while learning just a bit themselves, then, I think you can be successful. Just keep it concrete and probably visual. But if you are asking more of the parents, then they might not be so satisfied and you will be inundated with questions that come from their deeper way of thinking and that won't have answers that the kids can grok. 

On the other hand, if you want to start with teens and older you should have a group that is much more uniform in their mental structure and abilities so it would make a wider variety of techniques possible.