Can हर दिन follow सलाद or does it have to come before?
Hindi has a rather free word order, so, yes, having सलाद before हर दिन won't make the sentence grammatically incorrect. Having said that, the order in the suggested answer sounds way more natural.
रोज़ and हर दिन are same thing. They can be used in place of each other
Har din pitar salad khata hai - This is correct.
And you can't har din at the beginning?