Is it correct to skip the hyphen in the sentence "El mi-a dat o floare." and to write like this:"El mi a dat o floare."?
No, you are obliged to use the hyphen for the reason that all the non-accented forms of personal and reflexive pronouns are necessarily linked by the hyphen with the auxiliary verb that follows them, regardless of the nature of the auxiliary. In your example, you must link "mi", the non-accented form of personal pronoun in dative case, which fulfills the syntactic function of indirect object, and "a", the form of the auxiliary verb "a avea" ("to have") which helps to create the past perfect tense in Romanian language, the correspondent of past simple tense in English.
Should I use an indirect object before the verb in the sentence "Je lui fais écrire un poème."? It doesn't come handy for me...
Yes, it's correct to use an indirect object in this situation and not a direct one as it would be convenient due to the fact that when the verb "faire" followed by an infinitive and a direct object or a direct object clause, the indirect object is absolutely necessary before the verb.
Speaking of communication, what is the basic rule of having a good conversation?
It depends on how you define the word "good", but we all desire to have more meaningful conversation and in order to achieve this goal you have to be an active listener and to not only wait for your turn to speak because you won't be able to make capital out of the information received with the aim of developing a flourishing and advantageous conversation for both.