If your questions concerns 'z', resp. 'z(e)', this single preposition (also used sometimes as a perfective verb prefix!) can be both genitive or instrumental, naturally depending on the context-:) For instance:
Jestem z Polski. = I am from Poland (genitive)
Hiszpania razem z Polską jest największym kraju w EU. = Spain together with Poland is the largest country in the EU. (instrumental)
On przybywał ze swoimi rodzicami. = He arrived with his parents. (instrumental)
The 'zE' is written/spoken with a final 'e' in order to elide the vowel with the following sibilant 's'.
ze forma partykuły: z, używana najczęściej przed wyrazami zaczynającymi się od grupy spółgłosek: Dostaniesz za to ze dwa tysiące. Zatrudni ze trzydziestu mężczyzn.
ze the form of the particle z, most often used before words beginning with consonants clasters, e.g.: Dostaniesz za to ze dwa tysiące. Zatrudni ze trzydziestu mężczyzn.
So, the only reason for using it is to facilitate the pronounciation of otherwise unpronounceable clusters of consonants.
Ze is only used when z would make a difficult combination with the first letters of the next word. They mean exactly the same, and behave the same grammatically.
It's the same with w and we. To make the next word easier to pronounce.
Z(e) is used as: 'from inside of something' or 'off something'. Od means: - 'from something's proximity' or - 'from the direction of something' or - 'from someone's possesstion into other's possession'
e.g. On przyjechał z Krakowa - he came from Kraków (he was in (inside) Kraków) on przyjechał od Krakowa - he came from the direction of Kraków (we dont' knoe where he was, but probably close to Kraków)
zejdź ze stołu - get off the table (he is sitting on it) odejdź od stołu - get away of the table (he's standing next to it)
Notice the preposition - prefix aggreement here: odejdź od, zejdź ze
