customize category page

Hi Community,

I really need your help.
I hope here is someone with a extensive knowledge and is able to help me.

I’m sorry my English isn’t really good but I hope it’s enough to understand.

My issue is all about the category pages:

I have a couple of categories. And each category is in my menu and links to the category page. On this category page is every blog post listet that belongs to this category. so far, so good.

1. Issue:
My category page does not have a page title. The page starts with the first blog post. How can I add a Titel to this page? And how do I edit this title afterwards?

2. Issue:
Customize the category page. Is it possible, to customize each category page individually?
e.g.: The category page “wx” should organize and show the blog post in a grid of to post in a row. Where the preview of the post consists of a small picture on the left and the post-Title on the right.

while the category page “yz” shows all post among each other.

is that possible? or is the style/layout of the category pages all the same and not customizable individually?

(my website isn’t online yet)