Translation:I hope that your brother is feeling better.
Yes. This is exactly the same thing as the old "wie geht es ihnen?", only we´re talking about your brother instead of you. The sentence in German is "how´s it going for X", so the "es" is as necessary as the "it" in that sentence.
Wow I will sound foolish but I have never paid attention to es in "wie geht es ihnen?" before. :) Maybe it is because I learned that as an idiom.. Thanks a lot! :))
I thought that too, but now I think twice. Hope he gets better means he is bad, but I expect that he becomes better. Is feeling better is already better.
I am bit confused with "ihrem". Should it not be "her"? And how would one say: "I hope that her brother is feeling better."
Capitalized, "Ihrem," it is the formal second-person possessive. To talk about "her" brother, you would simply not capitalize it.
Because it is the subordinating conjunction ("daß" = that), not the article ("das").
I think that I hope your brother gets well, should be acceptaable. After all we don't say get better soon. We say get well soon.