Old English feallan (class VII strong verb; past tense feoll, past participle feallen) "to drop from a height; fail, decay, die," from Proto-Germanic *fallanan (source also of Old Frisian falla, Old Saxon fallan, Dutch vallen, Old Norse falla, Old High German fallan, German fallen, absent in Gothic).
These are from PIE root *pol- "to fall" (source also of Armenian p'ul "downfall," Lithuanian puolu, pulti "to fall," Old Prussian aupallai "finds," literally "falls upon").
Meaning "come suddenly to the ground" is from late Old English. Of darkness, night, from c. 1600; of land sloping from 1570s; of prices from 1570s. Of empires, governments, etc., from c. 1200. Of the face or countenance from late 14c. Meaning "to be reduced" (as temperature) is from 1650s. Meaning "die in battle" is from 1570s. Meaning "to pass casually (into some condition)" is from early 13c.
To fall in "take place or position" is from 1751. To fall in love is attested from 1520s; to fall asleep is late 14c. To fall down is early 13c. (a-dun follon); to fall behind is from 1856. Fall through "fail, come to nothing" is from 1781. To fall for something is from 1903.
To fall out is by mid-13c. in a literal sense; military use is from 1832. Meaning "have a disagreement, begin to quarrel" is attested from 1560s (to fall out with "quarrel with" is from late 15c.).