conocer is an irregular verb and the irregular verbs must be memorized http://www.spanishdict.com/conjugate/conocer although there is also a rule about c's and vowels. As far as the 'a afterwards' it is really an a - the personal a - used before people references. see here: http://www.bowdoin.edu/hispanic-studies/tools/newgr/ats/21.htm
Estelle0 I wrote "No conozco a tu novia." Cannot believe this is marked incorrect. The Duolingo person who marked this wrote as follows: "You missed a word"--followed by the sentence as above with the word 'no" underlined--if I missed it why is it underlined????? PLEASE let me know how to report this!!