I am not asking for translations, but how the word itself is related to words in other languages and what those words have come to mean like how "shit" is related to "science". I would really appreciate it if you could explain the reasoning behind why the words evolved in different ways.
There are no really secure cognates outside the Germanic languages (see, e.g., The Wiktionary entry expressing the doubts about outer-Germanic relations). A maybe unexpected English cognate is fidget (see http://www.woerterbuchnetz.de/cgi-bin/WBNetz/wbgui_py?sigle=DWB&lemid=GF04100 )
One can try to relate the f-word with Latin pugnus "fist", pugnare "to fight" and German fechten "to fight, to fence", Greek πυκτεύειν "to fist-fight". With this, more cognates can be derived (e.g. German Faust "fist").
From the Oxford English Dictionary:
Probably cognate with Dutch fokken to mock (15th cent.), to strike (1591), to fool, gull (1623), to beget children (1637), to have sexual intercourse with (1657), to grow, cultivate (1772), Norwegian regional fukka to copulate, Swedish regional fokka to copulate (compare Swedish regional fock penis), further etymology uncertain: perhaps < an Indo-European root meaning ‘to strike’ also shown by classical Latin pugnus fist (see pugnacious adj.). Perhaps compare Old Icelandic fjúka to be driven on, tossed by the wind, feykja to blow, drive away, Middle High German fochen to hiss, to blow. Perhaps compare also Middle High German ficken to rub, early modern German ficken to rub, itch, scratch, German ficken to have sexual intercourse with (1558), German regional ficken to rub, to make short fast movements, to hit with rods, although the exact nature of any relationship is unclear.
On the suggested Indo-European etymology (and for a suggestion that the word was probably a strong verb during its earlier history in English) see especially R. Lass ‘Four letters in search of an etymology’ in Diachronica 12 (1995) 99–111.
Note the copious use of "probably", "perhaps" etc.