The first main point to make in answer is : beware Newton myths -- there are far too many of them, and people have made money and (flaky) reputations fabricating catchpenny fake history about Newton.
The 'apple' story has been plenty embroidered over time. But there is a source, a notebook handwritten by Newton's friend William Stukeley. It was written possibly a long time after Newton in the 1720s in his old age appears to have told a reminiscent story to Stukeley. It is impossible to say whether the story in the notebook was itself embroidered, but the notebook can be read in scanned form at the Royal Society website at
https://ttp.royalsociety.org//ttp/ttp.html?id=1807da00-909a-4abf-b9c1-0279a08e4bf2&type=book
and the story about the apple as recorded by Stukeley reads (in part) as follows:
“After dinner, the weather being warm, we {i.e. Newton and Stukeley} went into the garden and drank thea, under the shade of some apple trees … he told me, he was just in the same situation, as when formerly, the notion of gravitation came into his mind. It was occasion’d by the fall of an apple, as he sat in contemplative mood. Why should that apple always descend perpendicularly to the ground, thought he to himself …”
It can be seen that the story is connected with Newton's ideas of gravitation only, not with his laws of motion. It seems that Newton thought of some influence of the earth extending upwards as far as the apple hanging off the tree, and he seems to have wondered how much farther up that influence might also extend, maybe as far as the moon? That seems to be as far as the initial germ of an idea went.
The origin of the laws of motion is a quite separate matter, certainly nothing to do with the apple story. Newton was aware of many previous contributions to possible laws of motion (and later acknowledged those he approved of, in the Principia). Various notes in the Newton papers show how he wrote and amended numerous sets of draft versions of laws of motion, worrying about this aspect or that, until it seems he was more or less satisfied. Tracing through them all involves consulting bulky sources and if you look for a good place to start, it is probably 'Mathematical Papers of Isaac Newton, Volume VI, 1684-1691' edited by D T Whiteside (Cambridge University press, 1974).