[6 War, p 17b]
Why Ambaa was after Bheeshm?
When Bheeshm went to Kaashee for Ambaa, Ambikaa and Ambaalikaa's Swayamvar, he had already declared that he was taking them for his half-brother Vichitraveerya; and everybody knew that he had taken the vow to remain lifelong Brahmchaaree, then why Ambaa was after Bheeshm to marry her? It was not justified to defame such a noble man.

By reading Mahaabhaarat it seems that initially Ambaa was not after Bheeshm. It was that man Akritvran, who came to that forest where Ambaa was staying, suggestively put the blame on Bheeshm, that "if he had not taken you from the Swayamvar... and since he is proud of his manliness that is why he should be punished".
-- This does not seem logical. Because taking away from a Swayamvar declaring that he was taking her for his half-brother is not a crime; besides if somebody has some kind of pride, that is also not a crime to be punished.

But perhaps Ambaa had a set of mind that if, and only if Bheeshm did not take her away from Swayamvar, she could marry Shaalv and Shaalv had also accepted her; but since Bheeshm took her away by force, and for the same reason she lost Shaalv, this was why she was blaming Bheeshm. This is true in a way, but in my opinion, it is not 100% true.

When Draupadee Refused to Marry Karn, Why Was She Ready to Marry a Braahman And Not a Kshatriya?
When Karn proceeded to pierce the eye of the fish, Draupadee refused to marry him saying that her Varamaalaa was notr for the neck of a Soot Putra. Then why did she get ready to marry a Braahman when Arjun in disguise of a Braahman went forward to pierce the eye of the fish from among so many Kshatriya princes and kings against the custom?

Was Draupadee Cooperative with Other Wives of Paandav?
NO. In fact when Draupadee agreed to be the common wife of Paandav, her condition was that she would not share her household with any other woman. In other words, disregarding popular practice of the times, the Paandav could not bring their other wives to Indraprasth. Arjun, however, succeeded in bringing only his one wife Subhadraa in Indraprasth, that also with a little advise from Krishn. She was Krishn's sister, Subhadra. He had to leave his other wives at their parents' houses.
This statement is wrong, see her statement G-4-Van/44, that she served Paandav along with her co-wives.