You can look at the class names of HTML elements in order to target certain types of pages. For example, the home page has a class name of "home" which you can see if you look at the page source. So if you put ".home" in front of your CSS selectors, then they will only affect the home page.
You can't add links using CSS only, but you can use CSS to change the appearance of links that area already on the page so that's what you'd need to do if you wanted to hide everything else but keep one line on the home page. Also note that CSS like this is theme specific.
Blaskan is a great theme. Good choice!
Here is an example I put together to illustrate how your idea could work on the Blaskan theme. Note that I've prefixed every selector with ".home" to just select the home page. I've also used ".home #nav li.menu-item-114 a" to target the 2nd link in the menu as the one to keep. I just picked on at random, if you wanted a different link, you should look at the page source, find the code for the menu, and change out the ".menu-item-114" part of the string with the class of the menu item you would like to keep. This example should also give you an idea of what kinds of things you can customize and hopefully it will put you on the right track to do a little experimenting on your own. :)
.home #header figure,
.home #site-name,
.home #content,
.home footer,
.home #nav li{
display: none;
}
.home #header {
border: none;
}
.home #nav li.menu-item-114 {
display: inline-block;
margin: 0 auto;
float: none;
}
.home #wrapper {
width: 100%;
text-align: center;
margin-top: 9em;
}
.home #nav li.menu-item-114 a {
background: none;
border: 0;
color: #000;
font-size: 64px;
text-shadow: none;
text-transform: capitalize;
}
Note that the next of whatever link you pick to keep for the home page in an example like this would be adjusted via the Appearance → Menus page.