1. I want to change the background to a gradient using css.
But I can't find where I should insert the css-code style.css!? I guess the code is (background: linear-gradient(180deg, #5FA831,#EBFFDE);)
Just a heads-up that you shouldn't be editing style.css directly, as all your changes will be overwritten when you update the theme.
If all you have are CSS changes, then you could use a plugin to add your custom CSS: 1) you can use the Jetpack plugin and activate the Custom CSS module, or, 2) you can install a standalone custom CSS plugin.
If you have theme edits in addition to CSS, you can create a child theme. If you want to go that route, you can explore these guides:
Your code should work when applied to the body tag, through your child theme or custom CSS plugin:
background: linear-gradient(180deg, #5FA831,#EBFFDE);
Because of CSS inheritance rules, if the above doesn't take effect you may need to add !important just before the closing semi-colon, so the code becomes:
background: linear-gradient(180deg, #5FA831,#EBFFDE) !important;
I just tested this on my end and it works. Let me know how it goes!