4) Should I take a look at the character and identify some strokes?
Strokes are for writing. Both phonetic systems Zhuyin and Pinyin are to help you denote and/or memorise the pronunciation. If you want, you can even denote every character in your Italian alphabet according to the rules you make. A Croatian fellow of mine learnt Chinese characters via Croatian alphabet (he simply ignored the Pinyin, Zhuyin and whatsoever, it never became an issue for him at all :D :D) all his way down.
Just remember, the Zhuyin-s or Pinyin-s should only come to you during this transition period. Sooner or later you will cast them away and use Chinese characters directly.
Here a suggestion for you, the problems the students who learn Chinese characters by Pinyin only are prone to have:
i) -ui is in fact pronounced like -uei, despite its standardised denotation -ui in Pinyin system
ii) the u in these three xu, ju and qu sounds very differently from its look as in bu, pu, mu . . .
iii) the i in these seven zhi, chi, shi, ri, zi, ci, si is quite another story as point ii).
iv) . . .
v) . . .
and so forth
I guess here is all I can answer now. I am a native speaker, TCFL and TCYL certificated teacher, but I am not interested to show this part of me on my italki profile here.
Anyway, hope it helps :-)