An opening hymn? What do you mean by that exactly?
In the Orthodox Church we use incense whenever it is called for at the services of Vespers, Matins, and the Divine Liturgy. It is not optional.
Fr David Straut
By opening hymn, I mean one of the so-called "paraliturgical hymns," many of which I think come from the Ruthenian tradition (at least, many of the melodies do). We sing it while the priest is incensing the icons and the church. This incensation takes place before he raises the Gospel book and intones "Blessed be the kingdom of the Father, and of the Son..."
The fact that you are asking the question makes me suspect that I am either using the wrong term for it, or that it is a latinization found in the ECCs, or in the Ruthenian Church in particular. I would like to know if that is the case. Are other ECCs using opening hymns? And what is the Orthodox practice?
As for incense, I've been under the impression that every liturgy should have incense. However, I don't actually know what the rubrics specify about this in the Ruthenian Church.