How to have a link look of non-<a> element?

You can use the classes btn btn-link. These are Bootstrap link styles that usually are found on anchor tags or button tags but if you use it on any other text it will use those styles on your text. It may not yield the exact same results so your CSS may need to be tweaked.

No. Non exists CSS class with link styles. If you open source code of Bootstrap you can find definition link styles for a tag.

bootstrap/scss/_reboot.scss

//
// Links
//

a {
   color: $link-color;
   text-decoration: $link-decoration;
   background-color: transparent; // Remove the gray background on active links in IE 10.
   -webkit-text-decoration-skip: objects; // Remove gaps in links underline in iOS 8+ and Safari 8+.

   @include hover {
      color: $link-hover-color;
      text-decoration: $link-hover-decoration;
   }
}