1. I want my grid layout to show only post picture and title, but not the introtext, is this doable? If I have to edit some PHP file to achieve this, which one is it?

You can disable that introtext from the Grid menu setting, you can check my attached screenshot below.

2.Is there an existing template can make the single category layout like this page: http://centraltv.us/index.php/%E4%B8%96%E5%8A%9F%E8%A7%82%E7%82%B9?

Unfortunately that is not possible to make it only show specific layout for single category page.

Yes, you can achieve this similar layout, you can check my 2nd and 3rd screenshot below.

#1: So in Easyblog->Settings there is no way to disable introtext? Maybe I will not just disable it for the grid layout but the also categories page or single author page.

#2: Because I will probably have to modify some PHP files to achieve the layout I want, I need some deeper understanding about this:
From the screenshots you gave me, Setting->Layout->Post cover has control over how the posts are displayed in a single category page(or other page), but what about themes? Theme files should also affect the page layout right? So I just need a clarification here: If I want to make some custom layout, all I need to do is create a new theme or modify an existing one, am I right? Do I have to also pay attention to other PHP files?

#1: So in Easyblog->Settings there is no way to disable introtext? Maybe I will not just disable it for the grid layout but the also categories page or single author page.

Yes, we do not have setting to disable that introtext from backend, you have to modify on this file JoomlaFolder/components/com_easyblog/themes/wireframe/blogs/latest/default.main.php

Then remove this line of code :

<?php echo $post->getIntro();?>

After that override this file into your current template location : JoomlaFolder/templates/yourCurrentTemplates/html/com_easyblog/blogs/latest/default.main.php

#2: Because I will probably have to modify some PHP files to achieve the layout I want, I need some deeper understanding about this:
From the screenshots you gave me, Setting->Layout->Post cover has control over how the posts are displayed in a single category page(or other page), but what about themes? Theme files should also affect the page layout right? So I just need a clarification here: If I want to make some custom layout, all I need to do is create a new theme or modify an existing one, am I right? Do I have to also pay attention to other PHP files?

It also depend on what theme are you using, but most of theme also will refer on this main theme wireframe.

In my opinion, I would suggest you that modify the existing theme file is better then you can override this file into your current template so you do not need to re-apply those customization code again for the future update.