There isn't a problem with the person travelling near the speed of light being a few seconds younger than us. If you were the one in the spaceship and it wasn't accelerating, the people on Earth would seem to be a few seconds younger than you. So both observers will see themselves being older. Relativistically, there is nothing wrong with that.
You are right. Two people travelling in a spaceship both at 99.9c will observe the other as travelling through time at the same rate as them.