Once you're on the lookout, go through the large dome in the center with Vegeta and Trunks. Once you're in the dome, go through the door in front of you, and you'll be in the time chamber! You can only be in it for one day, but it'll be good training.

Fighting for Sake of Evil: You receive negative Karma. Fighting for Yourself: You receive neutral Karma. Fighting to protect others: You receive Positive Karma.

Your grow stage can be set in the Character Creation menu. you can choose from any of the four growth stages when creating a character and afterword, the game will try and give you a fitting age for your growth stage. (though at this point in the game that might be a little glitched more research is required.)