this selectors not work exactly like jquery:
1- div.Content ~ div
2- div.Content + div
3- #div1 > div
Personally, I do not like these dot syntax selector styles, and they were implemented before me. In fact, I am not sure exactly what the syntax you provided is supposed to do.
Please explain each one so that I can tell you how to accomplish it using the other methoids that simple_html_dom has available to you.