I am brand new to Xcode, and I am also brand new Objective-C programmer.
I was wondering if it is possible to create simple Mac games with Xcode. If it's not possible, could you recommend me some good, cheap game engines?
Xcode can indeed be used to create games. You can do anything a Mac/iOS device is capable of by programming in Xcode.
I think you should focus on what part of the project you want to focus on. As you state you are a brand new Objective-C programmer (welcome). In my opinion it would be quite a mouth full to try and just into Objective-C programming whilst taking on Xcode AND game development (starting with engine design continuing with game design).
If the purpose is to write great games - get a nice engine that fits your needs (3D/2D/??) - have a look at Unity if you like. If the focus is actually learning programming Objective-C and/or Xcode I'd recommend that you make some small utility programs before jumping on to game development. If the point is to simply do game programming consider the alternatives to Objective-C and Xcode - pure C/C++ or even Java.
All that said - I wish you the best of luck in your adventure!
If you'd like to learn Objective-C, I suggest you have a look at cocos2d. It's an open-source 2d engine (written in Objective-C) that allows you to write games for iOS or Mac OS using XCode.
It's not as easy to create games with as with a package like Unity, but there are lots of tutorials (and even books) for cocos2d to be found. A good place to start with lots of tutorials is Ray Wenderlichs site.
Absolutely! XCode is the standard programming IDE for the Mac and iOS. So if your goal is making a game for iOS, you will probably be using XCode along with a few other helping technologies of your choice (e.g. OpenGL ES 2.0).
But since you mentioned game engines I'd also recommend you to use one, since they'll save you a lot of time and effort:
If you are planning to make a 2D game take a look at Cocos2D ( http://www.cocos2d-iphone.org/ ). It's quite popular.
And if you're planning to make a 3D game, maybe Unity ( http://unity3d.com/unity/ ) would be a good bet for you. It's not Objective-C but it can publish for iOS too, if that's your goal.