Sounds like you need a fume extractor!

Yes, that's the usual approach. Mylar sheets for short runs, stainless steel sheets for production. 3D printing in PLA probably won't have enough dimensional accuracy for fine pitch boards or boards of any size. The demo shown is a very small coarse pitch board.

The thickness of the stencil matters, because that determines how much solder paste you are laying down. This approach is going to produce thick stencils.

There are CNC machines for laying down solder paste. Here's one.[1] It does a few more jobs, too. The various CNC desktop board-making machines are still too expensive for most hobbyists, though.

[1] https://www.voltera.io/products/v-one