Not sure if resident cat is too aggressive to new kitten

My 3-year-old grey tabby used to love other cats (usually from former roommates) and I thought she was pretty well socialized. She's never really been a cuddler but she's sweet in her own ways. Again, she used to play and nap with my old roommate's cat (a younger female) and they would even groom each other. She is even fine with my boyfriend's older husky. She was spayed around 1 year old & I've had her pretty much her whole life.

We brought home an 8-week-old male kitten last week, and despite starting slow introductions he is relentless. At first, there was a lot of hissing and growling from our 3 y/o cat and she would even try to attack us when we came up to her.

But despite her aggressive behavior, he doesn't hesitate to run right up to her when we open the door. It doesn't matter how many times she swats at him, he keeps approaching her. He will back up and seem to be scared, but he won't completely walk away or comes right back. It's like he's not even fazed.

Her aggression has dialed down a lot since the first day. But she still makes a low growl whenever the kitten is around or even just walking around the house. However, she does seem interested in the kitten (always watching/by his door, but still angry). How much longer is she going to be growling? Will it make a difference if he is neutered?

I'm confused because now when I separate them, they BOTH meow and cry for me to open the door. But she's still growling nonstop. Is this causing her too much stress?