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First of all. Browse around here for a while, use the search feature, read up on old posts and you will find many different answers to your questions.
I want to ask that, can I earn money from the adsense for search? If it can, how?
As for your second question, about PSAs there can be a ton of reasons, from your account bein too new, the Google Mediabot being locked out from your pages (check your robots.txt file), your pages bein in a topic where there are few advertisers, your pages not displaying enough text for Google to be able to target ads...
As I wrote above. Browse around. Read a lot, and you will probably find the accurate answers.
I want to ask that, can I earn money from the adsense for search?
Yes. On my site, the CTR and effective CPM for AdSense search ads are extremely high. (Unfortunately, not too many of my visitors use internal search!)
If you have a lot of search traffic, you might be better off using your own search tool with regular AdSense ads on the results pages. Some publishers have reported good results with that approach.
I believe from the Adsense TOS, you're not supposed to put regular adsense ads on search results pages, whether they're internal to your site or not. That's why they gave us adsense for search.
That used to be the rule, but it was changed a number of months ago.
However, the program policies do include a definition of "competitive ads and services" that's worth noting:
"If you have elected to receive Google search services, this would include other search services on the same site and non-Google query-targeted ads."