BSOP VC BSP

BSOP is Black Scholes Option Pricing. BSP is not a standard abbreviation for anything to do with finance (I can only assume that you have seen someone use it as shorthand for BSOP!).
(There is something known as the Binomial Option Pricing Model (BOPM) which is used for valuing american style options (Black Scholes is only for european style options) but this is not examinable in P4.)

The interest rate is relevant because the term e^-rt in the formula is effectively discounting the exercise price over the time to maturity (it is continuous discounting rather than the yearly discounting that we usually do with NPV’s). It clearly makes a difference when the exercise price would be payable.

Usually we assume cash flows arise at yearly intervals and discount for whole years.

In practice most cash flows will arise continuously throughout the year and it would be more accurate to discount on a daily basis, or (obviously completely unrealistically) on a per second basis.

Continuous discounting is assuming flows arise continuously throughout the year and not just at yearly intervals.

(However, that is completely irrelevant for P4 except insofar as that is the reason for e^-rt )