Short answers, pulled from the story.
An adposition is a class of words used to express spatial or temporal relations, such as in, under, towards, and ago, or to mark semantic roles, such as of and for. The most common types are prepositions, which precede their complement, and postpositions, which follow their complement.
A preposition appears before its complement, as in English "under the table", while a postposition follows its complement. Languages such as Turkish, Hungarian, Korean, and Japanese typically use postpositions rather than prepositions.
Preposition stranding is a syntactic construction in which a preposition appears somewhere other than immediately before its complement, as in "What did you sit on?" It is common in English and North Germanic languages. The prescriptive rule against ending a sentence with a preposition was borrowed from Latin grammar and has no genuine basis in English usage; Otto Jespersen argued against it in his Essentials of English Grammar, first published in 1933.
A circumposition consists of two parts that appear on either side of the complement. Northern Kurdish (Kurmanji) provides clear examples, including bi...re meaning "with" and di...de meaning "in". English constructions such as "from now on" are sometimes analyzed as circumpositions.
Inflected adpositions, where the adposition changes form for grammatical person or number, are found in Celtic languages including Welsh and Irish, in Semitic languages including Hebrew, Arabic, Assyrian Neo-Aramaic, and Amharic, in some Iranic languages including Persian, and in Bororo, an indigenous language of Brazil. Spanish and Portuguese retain inflected forms in words like the Spanish conmigo, derived from the Latin mecum.
Simple adpositions are single words such as on, in, and for. Complex adpositions are groups of words functioning as a single unit, such as in spite of, by dint of, and in lieu of. The distinction is not always clear-cut; many complex adpositions developed from simple forms through grammaticalization, and German orthographic conventions acknowledge this ambiguity by permitting two spellings for certain prepositions, such as anstelle and an Stelle.