It's really common for even FT babies to not hold their own bottles until around 10 months, so adjusting for prematurity, it can be a year or so. I can't remember how old DD was, but it took quite a while.
My DD is 5 months, and she doesn't...but DH just hands it to her...and so then she's holding it. I'm like, um, she's not really doing it, as it slides to the side, but he just can't wait for her, I guess. We usually just give her 1 ounce so she can take her meds and I usually put it in one of those little pumping tubes that come with the Medela and so it weighs almost nothing, and she can kind of hold this.
My DS didn't start really holding it on his own until 11 months actual. I also didn't push him with it. I figure he's going to be independent soon enough.
Re: Bottles
It's really common for even FT babies to not hold their own bottles until around 10 months, so adjusting for prematurity, it can be a year or so. I can't remember how old DD was, but it took quite a while.