In Mockingjay Part 1, does it have katniss and peeta momment ?

yes it does and it was great and in one of the scenes some slob came from peeta and katniss mouth on the apuntalar, costa scene

In the movie, it has this great and heart-felt moment where Peeta is trying to strangle the life out of Katniss, but in part 1 of the book, it doesn't.

It has several one-sided moments but they don't interact much because of the plot of that half of the story.