"For the first time I have seen a lion."
Translation:Pierwszy raz zobaczyłam lwa.
What's the difference between widziałam and zobaczyłam?
And why can't „po raz pierwszy” be at the end of the sentence, like „Widziałem lwa po raz pierwszy”?
The sentence you suggested is totally correct and equally good with the default translation.
Please answer the preceding question about the verb change. What is the difference? Is it the "po" that makes one appropriate and one not?
Also, can one use "po pierwszy raz" or only "po raz pierwszy"? Does word order matter here?
It does matter, so 'po pierwszy raz' is wrong. But you can omit the 'po' actually, without changing anything in the meaning, at least IMHO. So the correct versions are:
po raz pierwszy
I'd say that "widzieć" focuses more on the 'process' of seeing. I saw the lion, I looked at it probably for a longer moment, I now know how it looks like.
"Zobaczyć" puts the emphasis on noticing the lion, on the moment when I first saw it. It's good for everything that you "suddenly" saw, but doesn't have to limit to that.
They have a lot of common ground, so they both perfectly fit here.