can i change the header image url for any category?

i have 2 categoies one named (beauty) and the seconds name (health)
plz i need help :

1- i wanna change the header url for every category , i mean when you finish reading any post in (health) category , then you click on the header image it goes to index.php , can i change it to make it go to the mother category (cat/health) not to the index?

2- the same with category page, i wanna change the header image url (on the top of category) when you click the cat banner gets you back to the same category page, i dont wanna go to the site index.php .

and if i know the steps for (health/cat) i will do them for (beauty/cat) also.