You can press Ctrl+L to select the location bar, Ctrl+K to select the search bar. You can set browser.search.openintab if you want searches from the search bar to open in a new tab and keyword.enabled to false if you don't want the location bar to be used for searches.
You can press / and type text to select any text with the Quick Find bar,[1] or press ' to select only links. You can use Ctrl+G or F3 in the Quick Find bar to go to the next occurrence of your search and Shift+Ctrl+G or Shift+F3 to go to the previous occurrence.
You can use smart bookmarks to go quickly to any website or make searches on any website by putting %s in a bookmark URL and adding a keyword which can be used from the address bar.[2] You can even add keywords that will do POST requests with the 'Add a Keyword for this Search...' context menu item for search fields.[3]
There are also many keyboard shortcuts for editing and selecting text in text fields, which have the benefit of being the same in most applications on all platforms. There's a list on Wikipedia.[4]
There are keyboard shortcuts even for the more obscure features, like Ctrl+Alt+R to enable reader mode and Ctrl+M to mute or unmute the current tab.
Your web browser already has good keyboard shortcuts, you just need to learn them.
[1]: https://support.mozilla.org/en-US/kb/search-contents-current...
[2]: http://kb.mozillazine.org/Bookmark_Keywords
[3]: https://support.mozilla.org/en-US/kb/how-search-from-address...
[4]: https://en.wikipedia.org/wiki/Table_of_keyboard_shortcuts#Te...