Well let's start off with the easy one which is 2. The nomination link doesn't naturally show up, you need to visit a page in the pet spotlight and change the setting for the pet in question from no to yes. just to note pretty sure nomination is not a heart but plain text link
So for number one, this is happening because of how css :target works. Your browser window isn't big enough to show the whole webpage to you but you also have overflow to hidden for the page itself so scroll doesn't appear. So when you click a tab you make one of the story elements target. Target is noted in the url, anyways the webpage will try to move the target to be at the top of the page, it "scrolls" the page as much as it can so in this case the amount of hidden overflow, and since it's hidden you can't scroll it back yourself.
It is quite a helpful feature, like that is how your story tabs work on a smaller scale when the page itself has no hidden overflow everything is fine. So how should you fix this, well here are two solutions that come to mind 1. make sure it fits on all reasonable screen sizes, or 2. allow scrolling on the page itself, or some combo.
If you need more specific help with it let me know