It's very common for the older child to regress and also to become extra needy at the end of a pregnancy and also when the newborn arrives. Somehow they sense that their world is changing and their time with mommy (and daddy) will need to be shared.
My favorite book is "Siblings without Rivalry". It's an easy read with lots of good information. Another good one is "Mom! Jason's breathing on me!"
As far as your day to day concerns, three's can be very "weird" to an adult but they are going through normal development phases. Mysterious, unenjoyable, yet common. I would suggest thinking about things from your son's eyes and it may help you with some new ideas or insights.
For example, with the cookie - imagine a most wonderful food right in front of you. You love everything about it, the smell, the look, the anticipated taste. Your excitement about eating it is barely containable. Then someone says "no. Don't eat it." You feel deflated. Your're told when you can eat it. And really look forward to that. But then that changes. And changes. And changes again. You're really confused. Then you're DENIED what's consumed your thoughts for HOURS!! Talk about disappointment!!!
I would see the lying only as an attempt to give you what you are asking for. At three, it's not a deliberate lie in the sense that we lie. Yes, tell him that it's not the truth and that you see his food not eaten, but don't think that your son is turning into a habitual liar. Not believing the lie and pointing out that it wasn't the truth takes care of that. (I know from experience this works.)
A good, but long book (and audiobook) is Nuture Shock - which is where I got the info to respond to the two paragraphs above. My local library had it.
Give your son lots of love and work on learning how to look at things from a different angle so that you're not constantly at odds with him. It really can be done. You can email me for more information, start reading the books above, add Playful Parenting and possibly Kid's are Worth It to the list and you're off to a great start. Also the yahoo group positiveparenting-discipline is great for this type of advice.
Hang in there! It's not an easy spot, but it does pass eventually.