If lot of resistance are connected in series then starting current and ending current is may same or not? But why. ....?

Think of pumping water through a tube. Assuming the tube is full, you get the same amount out that you put in. There's no other way for it to work!

In this case the negative terminal of the power source is grounded. But no current can go to ground, because the power source has to have the same amount of current coming in as going out.

The same. Conservation of energy means charge is conserved. Look up the definition of current and you will see why this fact is important.

In contrast, resistors connected in parallel have different currents through each resistor, because charge splits (though the sum of the currents through each resistor in parallel equals the current before it was split).

If you mean the current at each end of the resistors, it's the same, because the same current goes out of the negative terminal of the battery and goes back in the positive terminal.