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I think you should go for CAML query or out-of-box filters instead of search to find items in specific lists. If you want to use search anyhow, You can create a scope for each list and create managed property for each column to search for. Then, you can see below how to form keyword query with the properties and scopes : ...

By default in SharePoint, when you have a seach scope drop down, it shows the current site in the scope. As you have mentioned for your subsite B, it should be "This site: B". If you have a list- "List 1" in your site B page, you might also get "This List: List 1". These all happens by default. Now, since you need other subsites in the same scope, you can ...