You 100% should be asking your designer these questions. If you don’t trust her, then you need to find another designer you do. In the meanwhile:

1. Is the style in a master bath now to have a door that swings in and out, rather than a sliding glass door? This would be for a shower only. No bath.

Sliding glass doors on showers are more old style. People got tired of goop and black stuff on the track no matter how hard and often they cleaned.

2. Is a curved soaking tub out of fashion? Mine is sort of an hourglass figure, fit for one person at each end. Designer tells me this is out of style. Is it? Anyone have experience reglazing a tub from off white to bright white? Does it last?

Yes it’s out of fashion. I also don’t like a standalone soaking tub. While an art statement, they are not easy to get in or out of, and not easy to clean around. People end up not using them, and that’s a lot of money for an unused art statement in your bathroom. I prefer a tub with a surround. Easy to get in and out, and you can set your candles and wine down, and really enjoy your hot soak.

3. Do black faucets show water spots as much as chrome? Thinking I should go with brushed nickel to avoid water spots.

Yes black faucets do. They also don’t have the bright gleam of polished chrome.

4. Stacked tile - does it collect dust?

I am not sure what I think of as stacked tile is the same as you. Stacked tile is a way of laying out tile in straight grids rather than offsetting them. Don’t know why dust would play a part. Anyway, stacked tile as a style came in hot and fast. I might be concerned it’ll go out as quick. Though I love how it looks in the 3rd pic I posted above in #2. But those are not too grid-lined nor narrow, so that helps.

This pic show the stacked tile look that is very of-the-moment now, along with its rain shower head which I also don’t recommend despite how stylish it is: