I'd like you to explain to me the use of the subjunctive after certain verbs such as "recommend". Where can I find further examples on line?
1)Hamlet asks Horatio to tell his story recommending that Fortinbras, prince of Norway, be elected King and then he dies.
recommend someone to do something (is this construction also possible?)
http://grammar.ccc.commnet.edu/grammar/verbs.htm#mood
This webpage explains "mood" very well. Mostly we speak and write in indicative and imperative moods (statements and commands), and we use subjunctive to express ideas that are not facts (yet!): the "what if" thoughts, the "would" and "could" ideas, etc. The 4 uses for subjunctive are explained well on that webpage. Be sure to click on the word Conditional for more examples.
What you are referring to (the recommending followed by "that") is the 4th use for subjunctive in this webpage's explanation.
Your sentence 1) is correct: "... recommending that ... be elected ... "
I've never heard or read a correct sentence with "recommend ... to do... " The verb needs "that" following it. And if you use the construction Hamlet recommends Fortinbras... then it means Hamlet is approving of Fortinbras for some action and is letting others know about his approval. (In other words, that construction sets up a different meaning!)
Let me know if you have further questions about subjunctive. It's not an easy concept, for sure.