The subject may be the object of the statement and it is often a noun or pronoun. The predicate tends to make a statement in regards to the subject and is generally a verb or adjective. No function words are utilized between the subject and predicate. The majority of the words you mentioned contain it. For instance:

头发长 (tóufā cháng): "头发" is the subject and "长" the predicate.
他书写 (tā shūxiě): "他"  is the subject and "书写" the predicate.

The order of the two constituents is fixed together with the subject preceding the predicate.
The first constituent of a S-P phrase is generally a noun or pronoun serving as a subject or the topic, as well as the second one, typically a verb or an adjective, would be the predicate describing the subject. For instance:
"我闻到…" (I smelt…) The pronoun "我" is the subject and "闻到", a verb
No function word whatsoever is used between the two constituents.
The second constituent is normally stressed in pronunciation.

In Mandarin Chinese, S-P phrase is used as the subject, predicate, object, attributive, adverbial adjunct and complement of degree.
他这样做不对 (tā zhè yàng zuò búduì)。He did the wrong thing. (As the subject)
他手指破了 (tā shǒuzhǐ pò le)。His finger is injured. (As the predicate)
我希望你成功 (wǒ xīwàng nǐ chénggōng)。I wish you success. (As the object)
您提的意见很正确 (nín tí de yìjiàn hěn zhèngquè)。The opinion you put forward is quite correct. (As an attributive)
他说得大家全笑了 (tā shuō de dàjiā quán xiào le)。What he said makes us laugh. (As a complement of degree)

TIPS:
The order of the two constituents in an S-P phrase cannot be reversed, for the reversion of order will bring about a change both in structure an in meaning.
The two constituents of an S-P phrase have to match; otherwise, S-P phrase won’t make any sense.
An S-P phrase can function as subject, object or attributive without being introduced by a pronoun.