You can omit "any" in questions and there will be very little difference. "Any" helps to quantify the object in question. Also, depending on your tone, I feel it can make the sentence sound "softer."

There is usually going to be a slight difference in meaning. Do you have children? We’re looking for someone willing to his risk his life. (Focus is on you) Do you have any children? If you do, we should put them in your will. (Focuses more on the children) Does he have money? (Might mean “does he have a lot of money?” depending on the context) Does he have any money? (Does he have some money or no money? Again, context would matter) Has he had any girlfriends? (Has he had any girlfriends, even one?) Has he had girlfriends? (Could mean “Has he had a normal number of girlfriends?”)

Oh Sorry, I see your examples. Either way is fine, you don’t need the word any, however, it’s just one of those things we say in english, even thought it isn’t needed in your particular examples

Yes, you can omit "any" in all those examples. Side note: If you are having dinner and there is a basket of bread, the normal think to ask would be, "Would you like some bread?" the formal way to ask is: "Would you care for some bread?"

Could you give me an example of what you mean?