wiring lights from existing light fixture
Most likely you can't tap into that light to power your new lights. It is probably all switched power in the ceiling, which would mean you'd have to use the same switch. To verify, turn off the breaker and see what wires you have in the ceiling above each fixture and at the switch (how many wires and what colors are they?).
There is a chance you have a "switch loop" and that the power is fed to the fixture before the switch. In this case, you could tap into it for some new lights on their own dimmer.