In response to your first question. In Russia, and various other countries, men and women have different last names. Romanov or Romanoff could be the father or brothers last name. Romanova would be hers/sisters/mothers.
So technically it would be Romanova but she’s also gone but Romanoff in the comics, not just the movies. Though that is kind of incorrect when you get technical.
And by technical I mean in terms of Russia, but then again I’m not Russian. I could be slightly wrong but I remember a friend explaining it to me months ago. She had given a similar answer when I complained about it.
And for the second question Natasha is an international Russian spy, she would have mastered the American accent and language. So no, it doesn’t bother me.