How can I add more system apps to a custom ROM?
Most of the time when a unpacked and modified ROM gets repacked, it will become unusable/unstable because it failed to get resigned with the proper key.

You need to have the zip package resigned from the original firmware key. That is why you are experiencing those hiccups. Also if any of the apps depend on libs and/or resouces, you would need to make sure they are in place as well - prior to repacking and resigning

For a decent write up take a look at this: http://androiddomain.weebly.com/build-your-own-rom.html. This will show one of the proper ways of repackaging a ROM.