"Until when can we send you the e-mail?" Although this situation sounds very unnatural to me. I can't think of a situation where you would need to ask for a deadline regarding an e-mail. You should always send the e-mail as soon as possible, so asking for a deadline implies that you are not going to send it quickly. Can you provide more context for that situation so I can help you better? As for the second situation, for pregnant women, we say they are "showing" when you can see the stomach growing. For other situations, it depends on the cause of the swelling, but "swelling" is probably the most common word to use.

The first one, I think it's better to ask this way: When can we email you? The second one, those signs on the pregnant woman's billy are called "Stretching Marks".