Oh, don't feel you have to let them cry it out (CIO) at all. There's plenty of research that supports "responsive" nighttime parenting (i.e. "responding" to your babies cries). For that matter, google "cry it out harmful" and you'll see there are plenty of reasons NOT to let them CIO. It's also known as "sleep training".
Your heart seems to be telling you to pick her up and soothe her, she's *certainly* telling you that herself, and anyone who tells you otherwise doesn't have to hear her crying out in the middle of the night, so their opinion doesn't count. (Besides, science these days says they're wrong anyway.)
I second the person who recommended "The No Cry Sleep Solution" but I'd also like to point you toward a great (free!) resource on infant sleep.
http://www.kellymom.com/parenting/sleep/comfortnursing.ht...
There's also lots of useful information there on what "normal infant sleep" really is, (like why infants sleeping though the night at 6 months have increased nighttime wakings at 9-12 months.)
Oh, and the feeding? Make both of your lives easier and stick to the pureed stuff until she's grabbing stuff off your plate. Gagging is a pretty low level biological reflex - gagging *before* swallowing is the body's way to keep them from choking when they *do* swallow. Her body is saying she's not quite ready yet - she *will* let you know.
Some babies reject all attempts of solid foods (even the pureed ones) for their first year! (Happened to my lactation consultant). Nutritionally, all they truly need the first year is milk, and anything beyond that is to get them interested in new tastes and getting their tummies used to more substantial foods.
All babies *do* learn to eat, and it doesn't do anything to "teach" this (if that's possible) a few months earlier or later, except maybe give yourself a few more gray hairs. More good ideas here:
www.wholesomebabyfood.com