1- in America you would say 'can I pet your dog?' in England you would say 'can I stroke your dog?'. 'pet' and 'stroke' mean the same thing. It would sound strange if you asked someone if you could 'touch' their dog. 2- yes, you would either say 'he is a cross between a husky and a bulldog' or you could also say 'he is a husky bulldog cross'.

Thank you Scott!

1. In America, you can also say "Can I touch your dog?" but "Can I pet your dog?" would be more common. We don't use "Can I stroke your dog?" here. 2. We use "cross between Husky and Bulldog" or "Husky / Bulldog mix" or more rarely "mix of Husky and Bulldog".