Babruvahana was a son of Arjun and Chitrangada who ends up killing his own father with an arrow. Uloopi the step mother of Babruvahana used a gem to bring Arjuna back to life.
I want to know how Uloopi was the step mother of Babruvahana and what happened to Chitrangada after Arjuna left Manipur? How could Bhishma and Babruvahana both being incarnations of the Vasu Prabasha exist at the same time?
The Arjun Vanvas Parva SECTION CCXVI tells us the story of how Arjun and Uloopi got married:
One day that bull amongst the Pandavas, while residing in that region in the midst of those Brahmanas, descended (as usual) into the Ganges to perform his ablutions. After his ablutions had been over, and after he had offered oblations of water unto his deceased ancestors, he was about to get up from the stream to perform his sacrificial rites before the fire, when the mighty-armed hero, O king, was dragged into the bottom of the water by Ulupi, the daughter of the king of the Nagas, urged by the god of desire.
To cut the long story short Ulupi convinces Arjun to fulfill her desire by spending a night with her:
Thus addressed by the daughter of the king of the Nagas, the son of Kunti did everything she desired, making virtue his motive. The mighty Arjuna, spending the night in the mansion of the Naga rose with the sun in the morning. Accompanied by Ulupi he came back from the palace of Kauravya to the region where the Ganges entereth the plains. The chaste Ulupi, taking her leave there, returned to her own abode. And, O Bharata, she granted unto Arjuna a boon making him invincible in water, saying, 'Every amphibious creature shall, without doubt, be vanquishable by thee.'"
Next Arjun travels to the east reaching the kingdom of Manipur where he met Chitrangada. Desirous of having her as his wife he agreed to her father, king Chitravahan's condition:
All my ancestors (one after another) had each a male child. I, however, have only a daughter to perpetuate my race. But, O bull amongst men, I ever look upon this daughter of mine as my son. O bull of Bharata's race, I have duly made her a Putrika. Therefore, one amongst the sons that may be begotten upon her by thee, O Bharata, shall be the perpetuator of my race. That son is the dower for which I may give away my daughter. O son of Pandu, if them choosest, thou canst take her upon this understanding.'
Arjun agreed and stayed married to Chitrangada in that city for three years. When the princess at last gave birth to a son, Arjuna blessed his son and took his leave from his new family.
So this establishes the first part of your question about how Ulupi was the stepmother of Vabhruvahan.
Coming to the next part about what happened to Chitrangada - she became the queen mother when her young son as crowned the king according to the SECTION CCXIX:
Freeing those sacred waters (from the danger for which they had been notorious), and giving the Apsaras leave to go where they chose, Arjuna became desirous of once more beholding Chitrangada. He, therefore, proceeded towards the city of Manipura. Arrived there, he beheld on the throne the son he had begotten upon Chitrangada, and who was called by the name of Vabhruvahana. Seeing Chitrangada once more, Arjuna proceeded, O monarch, towards the spot called Gokarna.'"
As for the last part Mahabharat doesn't call Vabhruvahana a Vasu but does so for Bhishma. Check out this section SECTION LXVII of the Sambhava Parva of Mahabharat that mentions the various gods and demons who came down to earth in the form of various characters of Mahabharat:
And from the curse of Vasishtha and the command also of Indra, the eight Vasus were born of Ganga by her husband Santanu. The youngest of them was Bhishma, the dispeller of the fears of the Kurus, gifted with great intelligence, conversant with the Vedas, the first speakers, and the thinner of the enemy's ranks.