It is accurate to state that the
yeni cheri were a renowned group of sufi mystics.
ottoman turks gained control of much of the balkans before they took constantinople.
osmanli turks first consolidated their control of the southeastern part of the balkans, given to them by the seljuks.
fourth crusade captured constantinople from the ottoman turks. seljuk turks conquered the ottoman turks.

1.- Yes, they were a category of soldiers that involved in the Sufi Mystics.

2.- Yes, the Ottoman Turks Empire gained control of a vast area of the Balkans before they took Constantinople, specifically the southeastern part.

3.- Not exactly given by the Seljuks, but by their decline.

4.- No, Constantinople was not captured from the Ottoman Turks during the Fourth Crusade.

5.- No, the Seljuk Turks did not conquer the Ottoman Turks.

Explanation:

1.- Janissary, or Yeni Cheri which means "new soldiers", were not a group but a category of soldiers of the Ottoman Empire, which involved in Mysticism, or Sufism as they called it. Yeni Cheri was part of the Sufi Mystics.

2.- The Ottoman Turks were part of the Ottoman Empire which was a Multi-ethnic state who were gradually controlling other Turkish states, then they started to dominate the Balkans. Between the  XVI and XVII centuries they were expanding through three continents, having power over a big part of the European southeast. They invaded Bulgaria, Serbia, Bosnia, Hungary, much of Albania and Croatia and then managed to conquer Constantinople in 1453.

3.- After the decline of the Seljuks, the dominium of the Ottoman emerged and they started taking control of the southeastern part of the Balkans.

4.- Constantinople was captured by the Fourth Crusade but it was under the control of the Byzantine Empire when it occurred (1202–1204), not under the control of the Ottoman Empire, who conquered Constantinople in 1453.

5.- The Seljuk Turks did not conquer the Ottoman Turks, instead the Ottoman Empire gain power due to the decay of the Seljuk Empire.