Is it beneficial for my new blog if I add its link to my older blogs, especially to those with Pagerank? Does it have a positive effect on my new blog in terms of link building? Or will the linking just be ignored by the search engines?
Linking own blogs is not a good idea. But, linking to it generally will give you some PR with SERP increase as well. Try not to do link exchange between your both blogs.
If your blog have diff. class C IP. It's work but you must make sure that Search engine view your site as other website.
i agree with zidit ... dont link to the same sites that are on your same class c ip. if youve got your blogs on different ip (e.g with diff host providers), then sweet, no problems!