The number of webservers on shared IP's (usually called "virtual servers") is most likely outnumbering the webservers with a dedicated IP addresses. So it's more or less the rule - not the exception - that different websites resolve to the same IP address. So no worries in that area.
However, please be cautious when it comes to so called "vanity domains"! As an example, if your site is about blue widgets, it may reside on bluewidgets.com. You may also register navybluewidgets.com and coolbluewidgets.com. Nothing wrong with that, als long as you decide for ONE of these domains to be the primary domain, and redirect(!) the other domains to the primary. If you make the website accessible at all the other domains too, you are running danger of getting a "duplicate content" penalty by the search engines.
Hope that helps.
site-1/productpage ---link---> mainsite/productpage
site-2/productpage ---link---> mainsite/productpage
site-3/productpage ---link---> mainsite/productpage
where site-1, site-2, site-3 and mainsite have different layout and (slightly) different content, but talk aubout the same thing?
If yes, then what you are planning to do is called a "linkfarm". This used to work great some 2-3 years ago (which in internet-terms is like the 1950ies), but does not work "quite so well" anymore, especially not from a single shared IP.
My honest suggestion would be to kick site-1, site-2 and site-3 and focus on good, continually growing content for mainsite.
relevant pages linked to a page helping the ranking
Still is and probably always will be important. But they don't mean links from sites owned and operated by the same person and created for the sole purpose of linking in.
They were less able to filter out such links and differentiate between them and 'genuine' votes for a page's quaity, as evidenced by other sites linking to it, a couple of years back but they are getting better and better at it now and you would most likely be wasting your time with your plan.
Here you go: 26 steps to 15k a Day [searchengineworld.com]