Translation:You do not know too much about your grandfather.
is the "too" here really necessary in the english translation? Cause it feels like the person is feeling bad about knowing to much about his grandpa, and someone in the family is comforting him by saying:" dont worry, you dont know TOO much about your grandpa".. :D you don't know much about your grandpa sounds a lot more natural
But příliš, which appears in the CZ sentence, doesn't simply mean "much."
Here it's like "too much," "that much," or "very much." One of its basic definitions is "too," and it has a feeling of excess about it. See, for example: https://glosbe.com/cs/en/p%C5%99%C3%ADli%C5%A1
Because the subject here is "ty" and the object is "tvůj". If the object belongs to the subject, we use "svůj", it is better style.
In the translation to Czech we would also accept "o tvém".
The "translation" shown for svem is his/my/hers but in the sentence it is "yours". How come?
Svůj always relates to the subject of the sentence. Here the subject is implicit TY/YOU, so it means your.