What settings should I use when recording my child's play in a dark theater? I am not sure whether this is a good question to ask in this forum or even if it is answerable. I'll let the community decide.

I am a complete newcomer to video recording having purchased my first video camera this week--a Panasonic HDC-TM900. In reading many various reviews I settled on this due to its supposedly great low light performance. I will be using this primarily to record family events the first of which is my child's play.

The stage of the play is fairly well lit though I do not know the lux. The rest of the theater, naturally, is quite dark. How do I go about recording the best possible video of the play with the the equipment that I have? 

Being a newcomer should I just leave everything at auto? Does 1080P vs. 1080i really make a difference in video quality? Should I try recording in 24 FPS (Digital Cinema Mode) to get a more movie like experience?

I do have two shots at this as there are two showings so I can experiment with one and adjust for the other; however, I am not sure where to begin.
I think if you leave the settings on auto it should do the job just fine. Especially if the reviews say it performs well in low-light, I don't think you'll have a problem with exposure. Personally, I've never used that camera, so I guess I can't say for sure. 

1080P vs. 1080i is just progressive scan and interlaced scan. I won't try to explain the differences fully – if you want to read up on it, have a look at this site. There are pros and cons for using both, but for your purposes I would suggest going 1080P, that way you won't have to worry about de-interlacing your footage. 

Not sure what they mean by Digital Cinema Mode, but don't shoot 24fps. That's mainly for shooting film. Shoot 25fps (I'm assuming you live in PAL world?) if you're in NTSC land, shoot 29.97fps (or 30fps).