The Greek Orthodox should use the exact same liturgy minus the prayers for the Pope in three of the litanies, though in practice they sometimes take lots of shortcuts. We are allowed to fill our Sunday obligation at any church where the Holy Sacrifice of the Mass or Divine Liturgy is said, including Orthodox churches - legitimate reasons given by the Pope for going to an Orthodox church are pretty liberal and broad, and specifically include “the desire to be better informed”, which would certainly count in your case.
The reason why statues are absolutely forbidden in all Eastern Catholic and Orthodox churches is that what is depicted is not the fallen earthly, humanly reality, but rather the transfigured, “deified”, heavenly reality. Hence to depict something three-dimensional or realistic-looking for us would be to deny the transfiguration of the world through divine grace.
As I said before, the way I like to think of it is that the Roman Church depicts the mystery of the Incarnation from the viewpoint of the world - hence churches are adorned with three-dimensional statues, the theology is very rigid, cataphatic, and philosophically grounded, and the mystery of the Eucharist is veiled in a reverential silence (the reverence and awe also being expressed through kneeling). In the East, the mysteries are depicted from the viewpoint of Heaven - all the images are stylized to represent the transfigured reality, the mystery of the Eucharist is veiled through an iconostasis depicting the heavenly host, the entire Liturgy is sung, the theology is more apophatic and emphasizes the paradoxes of the Faith, reverence is expressed through standing, and the congregation gets blessed (and makes the Sign of the Cross) hundreds of times (153 is the traditional number of times the priest and congregation are supposed to make the Sign of the Cross during one Liturgy) rather than just once or a few times as in the West.
Also, in the West statues are regarded simply as psychological or sentimental aids to devotion, whereas in the East icons are actually sacramentals - they actually make present the heavenly mysteries they reveal. Statues don’t do this. It looks silly to incense a statue, but every icon in the church will be incensed several times in each Liturgy.