To answer your first two questions, the AJAX Search APIs were a family of APIs which included what is now called Web Search, Blog Search, Local Search, Book Search, Patent Search, Image Search, and Video Search. This family has now been deprecated as Google is building APIs on a new infrastructure. While replacements for most of these individual APIs have not been announced, the successor to the Web Search API is the Custom Search API, and the successor to the Local Search API is the Places API. Note that these are not true replacements because their functionality is not exactly equivalent. You can sign up for both the Custom Search and Places APIs through the API Console, at
http://code.google.com/apis/console
To build an app in which you display map markers filtered by category, you are probably going to want to use the Places API. In fact, this API is just about perfectly suited for such an application. You can find the documentation for the Places API, which should help you answer your fourth question, at the link below:
Jeremy R. Geerdes
Generally Cool Guy
Des Moines, IA
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