The founders of New Skete were under the Bishop of Albany because they were canonically Latin Catholics. This group was made up of who Latin Catholic Franciscans who decided to adopt the Byzantine Tradition. They were related to the New Canaan Friary but were not "native' Byzantine Franciscans. After they adopted the Byzantine tradition they sought to come under the Bishop of Passaic but he didn't want them (probably becasue they were, ironically, not Latinized) so they remianed under the Bishop of Albany until they felt compelled to join the OCA.
Before coming under the jurisdiction of the Latin Rite RC Bishop of Albany, Lance, the New Skete Monks and Nuns seem to have had, at the very least, a special liturgical/ritual relationship with the Ukrainian Greek-Catholic Bishop of Stamford, CT, Basil Losten, a relationship which continued until their formal reception into Orthodoxy via the OCA. Whenever it was felt that a monk needed to be ordained to the diaconate or priesthood to serve the community, it was Bishop Losten who traveled to New Skete to officiate. I have photos of such ordinations in old copies of New Skete's publication, "Gleanings."
As far as the lack of head coverings on the New Skete Nuns in the photos, *some* of the nuns occasionally wear a skufya with their riassas when entering the church, but remove them during Services. However, for the most part, New Skete nuns wear their riassas (and skufyas) *only* when in their own church or at a function while visiting another Orthodox church or seminary. Outside of church on their monastic property or at off-property worksites, the Nuns normally wear secular clothing, with a penchant for out-of-style pantsuits in pastel colors.
Btw, the same thing goes for the New Skete Monks: They usually wear their riassas (with or without skufya--I have never seen a New Skete monastic wearing a klobuk) only within church. Outside of church their dress is indistinguishable from lay dress, except when visiting a parish, another Orthodox monastery or a seminary.
I have visited New Skete less and less frequently over the years. Each time I have visited in more recent times, I leave feeling more empty than when leaving at my next most recent prior visit. I have this sinking feeling that New Skete, if it ever really had it to begin with, is losing whatever Orthodoxy it has left. I pray that His Beatitude, Metropolitan Herman's visit was not too late to stop further erosion of whatever they still maintain of the Orthodox Faith, which some of the monks blatantly say is the same Catholic Faith espoused by the Church of Rome, that the two Churches, Roman Catholic and Eastern Orthodox, are one and the same Church, only "temporarily DIVIDED!"