Was Tania - Zhivago and Lara's Daughter?

Probably.
The balalaika bit strongly suggests it.

"He was a poet, a scholar and a mighty warrior."

What Old Aussie said. It's strongly suggested in the book, too, though the whole part of about Lara and Yuri's daughter is handled very differently.

The balalaika - besides being a unifying symbol, reflecting back to the beginning of the film and the death of Yuri's mother - links the first scene to the scene with "The Girl" by the very words Yevgraf concludes the film with - "Ah, then it's a gift!" (referring to Tanya's ability to play the balalaika without having been taught). This concluding line harks back to the words of Anna to the boy Zhivago, when she tells him his mother had "a gift," and maybe he, Yuri, has it. Child Yuri rejects that idea. But the ending intimates that although Yuri had a different gift, he passed on his mother's talent to his daughter. There's a thematic circularity here.

There are other things that suggest that Tanya is Lara's daughter. As Yevgrav points out, the fact she was lost in Mongolia at the same age as Lara's daughter, that her "father" intentionally lost her in the mayhem, and that her name is the same as Lara's daughter's name, stretch the likelihood of coincidence, though they don't rule it out. Then Yevgrav asks her if she ever remembers her mother being called "Lara," and she says no, she doesn't think so. What Yevgav didn't know (but the audience knows) is that Komarovsky never called Lara "Lara," he called her "Larissa." So indeed, Lara's daughter would not have heard her called by that name. These are little things, but reinforce the idea that Yevgrav has found the right girl.

In the book, it's a little more definite that she is the right one, but of course without DNA and birth certificates, there would have been no way to "prove" anything anyway.

Jesus. When Lara leaves with Komarovsky, she says, "I'm carrying Yuri's child." Did you need it in neon?