I want to make a facebook page and I want to know when a post a link to a website will it show up on all of my followers newsfeed, someone said you have to pay facebook for that
Yes it'll show up especially if you are receiving any engagement from that certain follower. But if this follower is unlikely to engage on your page even if he/she likes it on the first place it will not show up on his/her timeline. On the other hand if you want to boost your post not only for your followers but for potential followers you can invest on ads.
Not necessarily. There are two newsfeed settings. Top Stories means the news feed has had some algorithm applied and the junk has been filtered out. The rules are secret but it will take in how often you interact with the source of the post and how much interaction it gets from others. Pages you have only just like or groups you have only just joined or people you have only just become friends with are, I'm expecting, more likely to come to the top. Most Recent used to mean you saw everything in chronological order but there is some filtering too as I know there are pages whose content I'm not seeing - but I'm not motivated enough to hunt them down.
What are the reasons why they do not all see posts? Is there a system being followed who sees and doesnt? besides those that unfollow?
Yes, there is a system Search on google and there will be tons of people offering advice on how to stay in people's news feeds - interaction appears to be the #1 factor You know this kind of post the more stupid "amen" comments they get the better placed they'll be with their next few posts in the newsfeed. Users either don't know or don't care. facebook doesn't care that the comments repeat the same string over and over - they don't look for "unique comments", just at the count.
It depends on numerous factors. From my personal experience (and many others) initially you will get very good reach but after a month or so the reach (number of people who see the post in their newsfeed) drops off significantly. It's probably FB's strategy of trying to get you to spend money on FB advertising.