Changing up the design a little

1) More info on how to change the number of circles in a row here:
https://www.ads-software.com/support/topic/edit-amount-of-circles-in-a-row?replies=2

2) Number of posts displayed can be changed in Settings > Reading in your Dashboard

3) You can use CSS in a child theme or a CSS plugin (like Jetpack) to do this. I recommend using Firebug for CSS work–makes it much easier.

View a particular category and look at the page source — the body tag has a class applied with a specific class for the category you’re viewing. So changing the background for a category like My New Category would look something like this:

body.category-my-new-category {
 background: #cccccc; /* or whatever color you want */
}

4) This is advanced and not something I can help with. You’d probably start by creating a custom page template that displays your posts by category instead of by date.