Is it possible, for example, to have a div that completely ignores CSS rules, no matter what classes and ids it contains?
Nope, this is (sadly) not possible without an iframe.
You would have to reset every existing CSS rule for that div like so:
div.sandbox
{
font-size: ....
font-family: ..........
margin: .........
padding: .........
line-height: .........
}
while difficult and never 100% reliable, it might be possible to achieve a usable result this way. You could look at one of the "reset stylesheets" like Eric Meyer's to get a list of important properties to reset; here is what claims to be a complete list of CSS 2.1 properties - excluding CSS 3 and vendor specific ones, which you would have to take into consideration as well.
Providers of 3rd party widgets often hard-code their "reset CSS" as inline CSS inside the HTML element to override any !important rules that threaten to override the sandbox class's rules.
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