PolyCrylic is water based. You never use natural bristle in water based products as the bristles rapidly swell up and go limp. The Purdy's should work fine. Foam can actually work fairly well if the work is totally flat. For very large flat surfaces, the applicators used by floor guys work well.

Nylon/polyester is what is recommended for Polycrylic, not natural bristle. Use the widest brush you have for large areas. Polycrylic levels very nicely. Work fast and away from direct sunlight and the results will be very good. Don't shake the can vigorously as this introduces bubbles when applying the product.

I've never used foam for this product, but I think it should work also.

Can I add a little water to extend the dry time?

Yes, 5-10% if you are in the 90F+. Otherwise probably not needed.

I've reduced about this about for spraying and it sprays very nicely.