"What else do you want?"
Technically yes, but while the original sentence is more directly translated to "in addition what is wanted?" Saying ほかに何ものがほしいです would be like saying "in addition something is wanted?".
It's a little awkward but could possibly be used if it seems like someone wants something specific but for some reason isn't being upfront or clear about it.
I have the same problem, and sometimes when I switch between options, new words will appear that I need to use (but other ones disappear that I needed). What I usually do is write the part of the answer that I can using the word bank, then switch to keyboard input, switch my keyboard to IME, and type in the rest. It's definitely more work, but I think it teaches you more. I just wish the progress bar wouldn't go so far backwards, or that they would give you more XP for using a keyboard. しかたがないよね？