I don’t get how medical family history works if a father has a stroke but he his son is already born and old does tht increase the chance ?

There are several reasons for checking a family history. First of all there are what are called predisposing factors. These are aspects of a person's genetic make-up, environment, etc. that can mean they have a higher probability of developing a disease. You are likely to have similar predisposing factors to your parents, especially genetic ones.

Then there are risk factors which are behaviours that increase the probability of a disease such as smoking, alcohol consumption, obesity, poor diet, lack of exercise, etc. While these are not inherited they are often copied. The son of a couch potato is quite likely to be a couch potato. It is not a given but it is a high probability.

The other reason for family history is about prevention. So if you have high blood pressure, eat a poor diet, smoke, etc. and there is also a history of stroke in a biological parent or other close blood relative your risk of stroke is high. What a physician can do with this history is give you advice on how to reduce your risk of stroke. Obviously they cannot remove your family history. However, they can get you to quit smoking, eat more healthily, take regular exercise, bring your BMI down, lower your blood pressure, etc.

Yes, it is in the DNA.

The factors that caused the father to have a stroke may be inherited by the son, but it makes no difference whether the father's stroke occurred before or after the son's conception or birth.