Is having a blog on Blogger beneficial to it's Google page rank?

To answer your first question, Blogger can help improve a site in the google search. But this is also true for any website owned by google, like wordpress. I am not sure what you mean about unbiased google searches.

Google searches are full of bias. There is an industry that studies how google displays its results (SEO - Search Engine Optimization) so google definitely does use bias. One way of improving a result is by having many different reputable websites linking to a page.

There is a little more science to it than I will explain here, but if you basically if a webpage has more incoming links than another page, it will rank higher. To answer your last question, so if your blogger blog is linked to your profile, that is another incoming link and will increase your Google profile by one more incoming link, possibly bumping it in the google searches. To answer your first question, Blogger can help improve a site in the google search.

But this is also true for any website owned by google, like wordpress. I am not sure what you mean about unbiased google searches. Google searches are full of bias.

There is an industry that studies how google displays its results (SEO - Search Engine Optimization) so google definitely does use bias. One way of improving a result is by having many different reputable websites linking to a page. There is a little more science to it than I will explain here, but if you basically if a webpage has more incoming links than another page, it will rank higher.

To answer your last question, so if your blogger blog is linked to your profile, that is another incoming link and will increase your Google profile by one more incoming link, possibly bumping it in the google searches.