With respect to your first question: it doesn't really matter how you register the scripts. You may chose whatever approach you like better.
Regarding the second question, RegisterStartupScript
on the script manager, it registers a startup script block for a control that is inside an UpdatePanel by using the ScriptManager control, and adds the script block to the page. In contrast, ClientScript.RegisterStartupScripts register a startup scripts with the page, it does not work with Ajax.
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