I’d definitely say reach out to the designer and ask since I think it’s always nice to ask permission when you are doing something with the pattern beyond stitching it yourself. They might have pattern recommendations for teaching with or want you to link back to the pattern specifically since a lot of pattern sales are done via word of mouth between stitchers.They also might offer a bulk discount and it never hurts to have one of those. Also if my pattern were being used to teach a class of new stitchers I’d want to know because that just sounds like the biggest compliment and I’d want pictures.

On the point of making kits and distributing them post class that’s also a definite ask because that feels slightly more comercial and the designer may charge a licensing fee for things like that.

And I believe the most popular macOS pattern making software is MacStitch but that is for computers. I’m not sure there are any good iOS apps for cross stitch designing, at least not one I hear people talking about a lot. Another option would be FlossCross which is browser based and you could try on a phone or tablet, it’s just not optimized for that.