If you have a new website and you install adsense on your site, will that trigger google to visit and index your site?
it wont make it any faster. But if your site wasnt already submitted to the 'sites to be crawled' list, it will be added.
as new website ... after the google crawler visit your sites. the easiest way is to make a link from already indexed page by google.
Yeah, ths right. but, if you use google webmaster tool to submit your site with a sitemap, tht'll help too.