Unfortunately i only started watching leverage during the last half of the सेकंड season, so i was wondering if Elliot and Parker ever had a relationship?

no, elliot and parker never had a relationship, elliot thinks parker is crazy
but hardison likes parker and parker has been giving off signs that she likes him too.

NO no no no no Parker & Hardison FOREVER!!!

ghousefan is right but plenty of people do ship the two together.