Interfaith dialogue refers to cooperative, constructive, and positive interaction between people of different religious traditions (i.e., "faiths") and/or spiritual or humanistic beliefs, at both the individual and institutional levels. It is distinct from syncretism or alternative religion, in that dialogue often involves promoting understanding between different religions or beliefs to increase acceptance of others, rather than to synthesize new beliefs.
Muslim is responsible to rectify himself and others as much as he can. Amr Bil Ma'roof and Nahi Anil Munkar is one of very important obligatory duties on every Muslim just like Namaz, fasting, Zakat, Khums, Hajj etc.
We must try our best to correct ourself and others as much as we can, but we have to be polite with others and never hurt their feelings. We have to have wisdom and good advice when calling people to the Way of Allah ( 16:125).
We are not allowed to be negative in front of wrong faith or wrong behaviour, because negative attitude can indirectly endorse or encourage wrong. We must try to do our best to help others and make them aware about the truth and never leave them indulging in wrong when we can help them. It is very important to do this responsibility with wisdom and good way of advice.
We respect every human being because Allah has granted honor to all human beings (17:70) and we feel for them and been ordered to help them as much as we can. Respecting others does not mean letting them do wrong, and accepting them does not mean accepting or endorsing the wrong.
Yes, you are allowed to. The Holy Prophet (s) used to draw up peace treaties with non-Muslims that respected mutual rights. When the Qur'an says 'do not take the Jews and Christans as your awliya'', it means 'do not make them guardians and managers for your affairs'. You can still communicate with them, and if they are your neighbours you actually must communicate with them in order to observe their rights.