I wish to produce a script that inspections for any new publish on the blogs server like gizmodo or something like that. It is possible to php function that may do that? or anyway whatsoever?

You could utilize RSS. RSS is XML. PHP can parse this. You will find many PHP good examples and "scripts" around the interwebs. Possess a look at different companies for PHP RSS readers and employ one that you could understand.

Obviously your blog you need to check should have an Feed. Most blogs come with an Feed or something like that similar: http://en.wikipedia.org/wiki/Comparison_of_feed_aggregators