Is what happened considered a promise that must be fulfilled, and does this promise become void by watching cartoon films that contain indecent scenes, and is this promise nullified if it is highly probable that the one who made it said "in shaa Allah" (God willing) at the time of the promise?

A servant's promise to Allah to abandon a sin is not considered an oath, nor does it necessitate expiation. However, abandoning sin is obligatory in all circumstances. TV series and cartoons that contain religiously forbidden elements, such as "kisses between sexes," are absolutely prohibited to watch. Whether oror not the promise is conditioned with "if Allah wills" does not affect it.