I think 'je sais' means 'I know' or 'I know it'. Since it also means 'I know it', does 'je le/la sais' exist? Or is it both possible?
Je sais means "I know". Normally you expect something behind (je sais + quelque chose), so it is completely correct to translate "I know it" with "je le sais" (skipping le is quite frequent in spoken language, but "je le sais" is the right construction.) Note that the it will be translated as "le" and not as "la", but "la" is possible in some cases, e.g. :
Je sais qu'elle est intelligente.
--> Je le sais. (le replaces "that she is clever")
--> Je la sais intelligente. (la replaces "she")