I've got some insert rules defined for my website, now I have to convert this into a multi site solution. My current insert rules apply to the new site. How can I restrict insert rules to work only on a single site in multi site environment?
You could create site-specific rules for insert options in /sitecore/System/Settings/Rules/Insert Options/Rules
For each rule you can select a condition (for a site-specific rule it would probably be 'where the item is the specific item or one of its descendants' for your site root) and an action (adding/removing specific insert options).
If you want to have custom rules per site and add them under each site node you could create site-specific folders with rules and override the default uiGetMasters/runrules processor with a custom class.
Site Specific Insert Option Rules For Sitecore https://www.markstiles.net/blog/2013/1/18/site-specific-insert-option-rules-for-sitecore/
All About Insert Options in the Sitecore ASP.NET CMS https://community.sitecore.net/technical_blogs/b/sitecorejohn_blog/posts/all-about-insert-options-in-the-sitecore-asp-net-cms
Insert Rules using Rule Magic https://trayek.wordpress.com/2013/05/24/insert-rules-using-rules-magic/