What questions would your character not want to be asked and why? Then get another character to ask said questions! Instant tension... instant conflict given they are, at best, going to resent being put on the spot like that and are bound to question the other character's reasons for doing so (well I would!).
It's also not a bad idea to ask yourself awkward questions from time to time. Why am I writing this? Is this the best way of writing what I want to say? Is my meaning as clear as I think it is? This, of course, is where beta readers can come into their own. It's also where honest reviews can be useful to the writer. If anything is puzzling your readers, it will come out in reviews (but they have to be honest reviews to be at all useful).