I was thinking about that too, so I found the words "Limette" and "Limone". While 'Limone' on googleimages gives pictures of yellow lemons (the same that appear when I searched for 'Zitrone'), only "Limette" gives pictures of green limes (the ones we use for caipirinhas in Brazil). So I figure Germans also have specific words for each lemon-like fruit, as in English, and 'Zitrone' doesn´t seem to cover limes.
No, that's completely wrong.
German "Z" (pronounced "tsett") makes a "ts" sound in all instances.
German "S" (pronounced "ess") makes an English "z" sound at the beginning of a word, except when it's part of the consonant cluster "SP" or "ST", where it makes an English "sh" sound, as in der Strand or das Spiel. In any non-initial position (with the exception of compound words), it makes a soft English "S" sound.
If S is in the middle of a word, then also it sounds like Z, is not it? It sounds like S only when it is at the end of a word. I might be wrong, I am only learning. I have got it from "http://joycep.myweb.port.ac.uk/pronounce/consons.html"
I'd like to clarify my earlier comment to say that S sounds like a "z" sound at the beginning of a syllable, not just a word. For instance, the s in "gestern" is a soft /s/ sound.
So yes, quite a lot of the time medial S will still be an /z/ sound. It's important but not a barrier to communication. So try to learn the right pronunciations while reading but also listen to Deutsche Welle podcasts and songs and talk with and listen to native speakers and you'll get the hang of it eventually. :)