How to show latest 10 posts as in category.php?

Hello WP users!

Maybe you can help me after days of searching I cannot find a solution!

What I want is to place a link on my site’s frontpage which leads visitors to the latest 10-20 articles which were published.

I want to show them exactly like my template does regarding categories.

Here is an example: https://simracing.hu/category/boxutca

So I want my latest articles to appear like on the link.

I tried playing with category.php which is responsible for the layout, and things, but I really don’t know what to do….

Here is the code of the php:

[71 lines of code moderated as per the Forum Rules. The maximum number of lines of code that you can post in these forums is ten lines. Please use the pastebin]

Can anybody help me in what I would like to reach?

Thank you very much in advance!