Does a drop in the voltage slows the flow of current or reduces the current Also in terms of electrons why does a drop in potential difference increase the voltage for the next resistor in series?

Answer 1

If there is less voltage across a resistor, there will also be less current.

As for the second question, I assume you mean two resistors in series. If the voltage or potential difference across one decreases, then the other one must increase, due to Kirchhof's Voltage Law: the total voltage across the two resistors must be equal to the voltage across the battery, which is usually assumed to be constant.

Answer

You can think of voltage drops in terms of a water radiator central heating system. In order to drive water around all the radiators, there must be a difference in pressure across the entire system. But for water to flow through each, individual, radiator, there must also be a difference in pressure across its input and output orifices. The sum of these individual pressure difference must equal the pressure difference across the entire system.

If you now equate a pressure difference across an individual radiator with the voltage drop across a resistor, then the sum of the voltage drops across each resistor must equal the voltage across the entire circuit.

You should also realise that voltage does not 'slow down' current -it affects its magnitude (in amperes)