Not only is this normal behavior for a month old, it's normal if he's still this way for many months more. The sleep, fussiness, hunger, everything, is all over the map during the first year. Count your blessings that he naps well during the day. That may not last either. So take advantage of that and get some rest for yourself too. So you'll be better equipped to handle his night time needs.
Don't assume he's hungry. If he had words, he could tell you exactly what he needs. He can't, so he cries instead. He may be just telling you he wants to he held close, or he's not sleepy. Cries do not imply hunger and don't be tempted to over fill his tummy (especially with solids or cereal) just to stop the crying. Overstuffed babies do not sleep better, the sleep worse cause they're uncomfortable.
Here are some links on normal infant sleep to give you an idea what to expect in the first few months. Expect him to wake often, cry even when he's not hungry, and basically be really needy, especially at night. It's all a part of the first year bliss! But as hard as they will be on you, they will pass quickly. Congratulations on your new baby!!
Newborn Babies and Sleep
http://www.kellymom.com/pantley/pantley03.html
Sleeping Thru The Night
http://www.kellymom.com/parenting/sleep/sleep.html
8 Infant Sleep Facts Every Parent Should Know
http://askdrsears.com/html/7/T070200.asp
31 Ways to Get Your Baby to go to Sleep and Stay Asleep
http://askdrsears.com/html/7/T070300.asp
Co-Sleeping: Yes, No, Sometimes?
http://askdrsears.com/html/7/T071000.asp
Sleep Problems: Answered!
http://askdrsears.com/html/7/T071100.asp
Studies on Normal Infant Sleep
http://www.kellymom.com/parenting/sleep/sleepstudies.html
And since you mentioned you may be concerned about constipation, here are some links on poop!
Chances are he is not constipated, especially if he's breastfed.
What's Normal
http://www.mother-2-mother.com/normal.htm#NormalStools
Infant Stool Patterns
http://www.umc-cares.org/health_info/article.asp?Category...
Poop
http://www.drjaygordon.com/development/pediatricks/poop.asp