When you search on IxQuick, the search results have a proxy version of the webpage that you can visit. It'll protect you from malicious scripts trying to install viruses or run on your computer from the website, because (I presume) you're viewing through IxQuick's servers. But how does it protect itself from the malicious stuff?

It's simple, because everything you are browsing is filtered, but that's not all .. you browse in an anonymous way, because they can't see where you are from, ..etc

When you search on IxQuick, the search results have a proxy version of the webpage that you can visit. It'll protect you from malicious scripts trying to install viruses or run on your computer from the website, because (I presume) you're viewing through IxQuick's servers. But how does it protect itself from the malicious stuff?

It's presumably possible to craft a malicious website that could infect their system. But a proxy service doesn't open the webpage in a regular web browser, parsing the HTML and constructing a page to display -- it just runs its filter over it and passes it on. Hence the normal methods of infection, like bugs in your web browser and browser plugins, aren't available for the proxy service. You'd need to write a different kind of virus to infect them, and that'd be difficult without having a copy of their software to test against.