Google can do (1) because they crawl the entire web constantly. That's not going to be a trivial feature to add for anyone else. (2) is also probably a side effect of crawling pretty much everything before you ask for it.
I too am looking for a reader with rss search. This was the main reason I gave up whatever desktop app I was using at the time prior to Google Reader
(1) It lets you add subscriptions to regular websites without an RSS feed.
(2) It lets you search for articles that were published before you subscribed to the feed.
I think you could add (2) simply by redirecting to Google search using the site:sitename.com argument.
(1) may not be that simple to add but it would be an incredibly important feature to have.