L.B.
She has always been very serious about when she eats because all babies are. Babies need to eat very frequently because their tummies are so little, and they empty quickly. Not only that, but most of us parents miss their early feeding cues, like rooting (moving their mouths around, licking their lips), so by the time they start *crying* to be fed, they're really hungry, desperately so.
Anyway, about your more general question: first of all, it's amazing that your daughter will let you put her down and leave her alone in basically a soft little box for as LONG as 30 minutes at a time. My daughter never did, either with me or my husband. And it's not really fair of us to ask this of them. They're vulnerable little babies, and when left alone, they feel like they could die if someone doesn't pick them up. And the reason is, in our evolutionary past, this was absolutely the case. Babies were never left alone before modern devices like cribs were invented. If they had been, they would have gotten eaten by predators or rolled down a hill or covered by bugs. So, babies have evolved the fear of being left alone. Besides that, the first 3 months are still, developmentally speaking, still feel to the baby like she should still be in the womb, because babies are born so premature, just because they're getting too big to stay there. So, they still feel like they should be wrapped up tight and in a moving, warm environment. Laying flat on a crib mattress without hearing mom's muffled but nearby voice in the womb feels very alien and scary. So, for those first three months, she really wanted you to hold, hold, hold her.
Since then, she has developed this habit of desperately crying for you because she has been deprived of this more secure transition to the world outside. (Some babies just transition more easily; they're not "good" babies while you might think you have a "bad" baby or a "diva" - there's no such thing as a bad baby. Your baby barely even knows her arms are her own at this point.)
The way to fix your "problem?" Hold your daughter more. Pick her up *before* you expect her to start crying. You need to change your expectations. Babies can't just be turned off and put on a shelf. Don't resent her for it. If you give her all of the love and security and comfort in your arms that she desperately needs now, she will be more independent later. It could be that your boyfriend is less quick to respond to your baby's cries, so she has learned to not cry for him to pick her up, but she knows that you will. This does NOT mean that you should "train" your daughter to give up on you both. In fact, you need to teach your boyfriend to hold your daughter more, and be more attentive to her, so that she doesn't grow up with a deeply felt belief that nothing she does has any effect on those around her - not even the two people who should love her the most in the world. Crying and getting no response does this to a child.
The first 5-6 months or so, I've learned, are just one big challenge to a couple. Feel grateful if you have family nearby who come to help. We didnt' even have that! All of my husband's and my family live out of state, far away. But that's just life. Parenting is hard, very, very hard. If it's really easy, you're not doing it right! And it never works, to try to do it the easy way, trust me. I've seen so many families in which the parents tried to do things the easy way, even though they knew it wasn't best for hteir children, and their children developed health issues, discipline issues, and even trouble at school. So, be assured that at least the extra effort you put in now will pay off in less effort and less heartache later.
Practically speaking, I recommend that you get a baby carrier like the Ergo or a Maya wrap so that you can carry your baby and keep your hands free. It's SO much easier than just carrying your baby around in your arms. and you will see! The more you hold your baby, the less she will cry in general.
For more information, read the Dr. Sears Baby Book or the Sears Discipline Book.
Hang in there. It gets a little easier soon. Especially once your daughter can sit up on her own and play with toys by herself. But don't think that means you an leave her to play by herself for more than a few minutes! LOL. Babies just aren't built that way in general.