If you entered your information in Czech then it will remain in Czech, because changing the language does not change the information in your tree. The chart gets the information from your tree. Only the title of the chart will change.
When you create a tree online, its data language is determined by the language of your site when it was created. I can see that the language of your site is Czech, and so is the data language of your trees. That is why the chart is in Czech. Things like the labels you specified won't change when you change the site display language- that can only change the language of the title of the chart.
Regarding the problem with dates in Czech, this is a bug in our site. The developers have been notified and are working on fixing this problem. I will update you regarding this matter, and apologize for the inconvenience.
Let me know if there is anything else that I can help you with.