For 3, you can also middle click the back button to reopen the search engine tab again.
- ctrl click the refresh button (any of the navigation buttons really, although they will clone the previous or the next in the history)
- middle click the refresh button
And my favorite: “yt” key combo when using Vimium-ff.
Additionally, it’s useful because I like to keep related tabs next to each other, so I often used these methods to duplicate a tab (or ctrl/middle click on the new tab button to open a blank one next to the current tab), but now I only need to press “t” to open a new blank tab right next to my current one.