1. The Zaire Use of the Roman Rite
Yes, those are spears. All male servers carry spears throughout the liturgy. The priest wears tribal robes, and the celebrants and servers jubilate around the altar as a means of reverence. The Use was established in 1988 by St. John Paul II.
2. The Syro-Malabar Church & Rite
Members of this church are direct descendants of the Thomas Christians that the Portuguese experienced in 1498 while looking into the Malabar coast of India. They did not break from Rome until 1653 as a result of obscene latinization that forced onto them since 1498. However, in 1923 Pope Pius XI set up a full-fledged Syro-Malabar Catholic hierarchy.
3. The Premonstratensian Rite or Norbertine Rite
The Premonstratensian, or Norbertine, rite varies from the Roman in the celebration of the Sacrifice of the Mass, the Divine Office and the administration of the Sacrament of Penance. The priest will say quietly what the choir sings, as is the situation with the Kyrie and Glorie.
4. The Ambrosian Rite
According to St. Augustine (Confessones, IX, vii), St. Ambrose did renovate sections of the Divine Office, so it is not inconceivable to trust that he is also the founder of the Rite of his namesake.
5. The Ethiopian Rite and Church
In a place that was closed from the Catholic Mission for 200 years, a rich tradition of liturgy has survived. The Church reunited (totally) with Rome in 1930, and has a decent presence in America. Pope Francis, himself, made a great impact on the church and its development remains active.