in 和 副詞

(1) I believe in destiny.

這裡的 in 不是副詞而是一個介詞。
believe + in 成為 phrasal verb 後跟名詞(組)

~ believe in somebody/something
meaning: to feel certain that somebody/something exists

相信命運的存在

(2) I will give you something for free. I will give you my watch for free.

"something" and "my watch" are the direct object of the verb "give".
"for free" is an adverbial prepositional phrase modifying the verb "give" to answer the question "how".
~ I wil give you something in a manner that I will not charge you any money.

但係我唔明點解可以加係名詞後面??

Adverb can be placed in different positions of the sentence depending on its nature. This kind of prepositional phrase is normally placed at the end of sentence.
其實係句子後面，只不過是句子結構的關係 (S + V +O)

另一句子結構 (S + V): 不及物動詞

The car runs in full speed. 就唔係係名詞後面

2014-09-11 06:18:05 補充：
不好意思，打錯字

The car runs at full speed. 就唔係加係名詞後面

Believe = think that someone is telling the truth or something is true (相信)
I believe your story.

“believe in” 是 verbal phrase (片語動詞) = verb + preposition/adverb,
信仰, 相信（…的存在); 信任;信賴
verbal phrase 有特別的含意
Do you believe in God?

2014-09-11 08:00:03 補充：
will give ~ verb phrase (動詞短語)

動詞片語是由主要動詞 (main verb) 與一個或一個以上的助動詞 (auxiliary verb) 所形成,用來表時態、語態、疑問、或否定
verb phrase 不同 verbal phrase

you 是 indirect object
something 是 direct object

f

2014-09-11 08:14:17 補充：
for free 是 adverbial, 功能係副詞

adverbial 通常是 prepositional phrase, adverbial phrase, noun phrase
作用相似副詞
一個字 adverbial 是 adverb

簡單些
I will give you something free
free 是 adverb

其他例子:
S + V + O + adverbial
He hit his friend at school.

S + V + O + adverb
He left town hurriedly.