Couple of questions

Hi @srdjancuric,

I hope you are well today and thank you for your questions.

First: How to remove author icon and name from post?

You can remove it by adding the following CSS code in the Custom CSS option of the latest version of Sparkling theme on the below path.

Admin Area -> Appearance -> Customize -> Sparkling Options -> Other -> Custom CSS

.entry-meta span.byline {
    display: none;
}
Second: How to increase font-size in the Menu?

You can increase it by using the following CSS code as described above.

.navbar-default .navbar-nav > li > a{
  font-size: 13px;
}
Third: Can I somehow blocked links to the posts in slider, when I click on slider title that do not open anything?

You can try achieving this by using the child theme of Sparkling theme shared in the following reply.

https://colorlibsupport.com/t/slider-with-link-to-the-post/#post-29446

Best Regards,
Movin