[minminRW]

- Why this Kanji: 樹 When 木 would also seems "tree" ? Or are i'm wrong?
　
木 and 樹 have almost same meaning. But 木 have wider meaning than 樹, 木 means sometimes lumber, board, or other wooden materials but 樹 means a live tree. And in the use of human name, 樹 is preferable.

木(on-yomi=boku,moku / kun-yomi=ki(gi))
木刀(boku-tou)Wooden katana
木製(mokusei) made of wood
　　
樹(on-yomi=jyu / kun-yomi=ki(gi))
植樹(shoku-jyu)tree planting
樹海（jyu-kai）ocean of trees


- It's depend on what if you write it in hiragana or Kanji? Are some words more write in hiragana, or it's just your own choise which to use?

for exanple, your question is like below in Japanese,
あなたがたは、何によってひらがなや漢字を書いていま すか？
いくつかの言葉は、よりひらがなで書かれたりするのか 、または単にどちらを使うかあなたの選択なのでしょう か？

simple rule is like as follows(but not strict)
1.noun:mainly used kanji except easy words or foreign words.
　　何(nani)-what、漢字(kanji)-kanji、言葉(kotoba)-word(s)、選択(senteku)-choice
2.verb,adjective,adverb:mainly used kanji and hiragana conbined like below.
　　書いて/書かれ=書く(kaku)-write、使う-use、
　　単に(tan-ni)-just *単-single/sinple(noun) + に-with = just/only
4.prepsition, suffix form, other short words or very easy words are mainly used hiragana.(many case these cannnot use kanji)
　　は(wa)-is(not verb in Japanese)、や/または(ya/matawa)-or、より(yori)=more
　　あなた（anata）-you、どちら（dochira)-which
*but in case of あなた（=貴方、貴女、貴兄）、or　または（=又は）,you can use kanji on your own choice.