Font size of post title on Home page

@Vitaliy:
1. To change the font size, you can add the following css in “Appearance => Theme Options => Custom CSS” box:

.home .entry-header .entry-title {
	font-size: 20px;
	font-size: 2rem;
}
@media screen and (max-width: 960px) {
	.home .entry-header .entry-title {
		font-size: 18px;
		font-size: 1.8rem;
	}
}

2. the quantity of post in homepage is controlled from your “Settings => Reading”. There is no option to controlled just for homepage.

3. I don’t get it what you mean rubric name.

@Vitaliy: That option is not there. So, you need to build child theme and then modify the loop functions.

There are post in your home page. One you have Featured Content Section and Another is latest posts. So, you might need to hire customizer to work on this.

Firs, you can download child theme from http://catchthemes.com/blog/create-child-theme-wordpress/ and then copy content.php file to your child theme and then add your category code before <h1 class="entry-title"> title tag.

@Vitaliy: You need to know about WordPress function for this level of customization. See this https://codex.wordpress.org/Function_Reference/get_the_category_list . IF not then you need to consider hiring customizer.