jsFiddle Demo
jQuery provides several selectors (full list) in order to make the queries you are looking for work. To address your question "In other cases is it possible to use other selectors like "contains, less than, greater than, etc..."." you can also use contains, starts with, and ends with to look at these html5 data attributes. See the full list above in order to see all of your options.
The basic querying has been covered above, and using John Hartsock's answer is going to be the best bet to either get every data-company element, or to get every one except Microsoft (or any other version of :not
).
In order to expand this to the other points you are looking for, we can use several meta selectors. First, if you are going to do multiple queries, it is nice to cache the parent selection.
var group = $('ul[data-group="Companies"]');
Next, we can look for companies in this set who start with G
var google = $('[data-company^="G"]',group);
Or perhaps companies which contain the word soft
var microsoft = $('[data-company*="soft"]',group);
It is also possible to get elements whose data attribute's ending matches
var facebook = $('[data-company$="book"]',group);
var group = $('ul[data-group="Companies"]');
var google = $('[data-company^="G"]',group).css('color','green');
var microsoft = $('[data-company*="soft"]',group).css('color','blue');
var facebook = $('[data-company$="book"]',group).css('color','pink');
<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>
<ul data-group="Companies">
<li data-company="Microsoft">Microsoft</li>
<li data-company="Google">Google</li>
<li data-company ="Facebook">Facebook</li>
</ul>