Hi Jimmy let me try to add some flavor to the answers:
Q1: Do Chinese people generally agree upon how a sentence should be segmented into its compounds?
Yes and No. Internet youngsters would disagree upon the normal segmentation of words and even use wrong characters to represent an added meaning to the original word, example:
我要和你生猴子
"I wanna give birth to monkeys with you". But it actually means "I wanna have babies with you", to represent the worship of the author by commentors. "猴子"monkey has a similar sound like "孩子"child.
普大喜奔
Is actually a compound internet word meaning “普天同庆，大快人心，喜极而泣，奔走相告”, consisting of 4 成语 words(Chinese Idioms with traditional roots) to mean the extreme thrill one feels about some tremendously great news, each meaning "Worth celebration by all people under Heaven", "Making people feel very joyful, usually after the resolution of some very bad matter", "So happy that I wanna cry out", and "Such a great news that I wanna spread it around all over the streets".
However, these words are not generally used in official circumstances.
Q2: Is a 词 different from a word in any sense?
Yes and No. In Modern Chinese language (taking root from Ancient Chinese language, emerging from Yuan Dynasty's everyday life, taking shape in 1800s with heavy influence from western languages, words, constructs, and even grammar, and formalized to be its current shape in 1900s), most of the Chinese 词 could have very good correspondence in western languages.
However in Ancient Chinese works or the very popular usage of them as 成语(Chinese idioms with traditional roots) in modern Chinese, we could see the segmentation of 字 as 词 much smaller than in everyday modern Chinese:
审时度势
This is a Chinese Idiom meaning to 审视(inspect, examine) 时局 (time, era) and 度量 (gauge, measure) 形势 (circumstance, context), and the whole Idiom means an attitude one takes within a complex circumstance, which stresses more on taking thorough considerations before taking wise actions.
And as you could see, more and more new internet idioms are being invented and circulated as the culture in China evolves, many of these taking direct root from 成语 (such as 普大喜奔), and most of them using smaller segments (one character) as 词 to shape a compound 词.
Q3: Do even native Chinese generally split characters into words (词), or is the concept of words something we have forced into Chinese because it makes sense in western languages?
Yes and No. Within the Chinese language itself there is a long history of moving from shorter words (1-character words) to longer words (2,3,4-character words). And the shaping of modern Chinese language is directly and heavily influenced by western languages to use western-origin compound words. Many of these words are firstly translated by Japanese scholars into Chinese compound words in Japanese language, then brought back to China. For example:
物理 化学
each meaning physics and chemistry. Literally they mean "the principles(理) of things(物)" and "the study (学) of transformation(化)"。
Personal thoughts:
as for me a native Chinese, I found the distance between grammars of Chinese and Japanese is larger than the distance between grammars of Chinese and English.
And more as I dive into the histories of the evolution and formation of cultures and languages, more I found the current versions of our cultures(western or eastern) all take influences from each other.
The Chinese language construct of character-word constructs 字词构造 make it very good as as future-oriented platform for cultures, subcultures and efficiency of communication to evolve and prosper. It is neat, yet meaningful. As long as one has mastered the basics of Chinese, non of the world's mysteries would be hidden to him/her in the shape of an 'unknown pronunciation' of an unknown word. True wisdom lies within the small fabrics of Chinese words, feeding the whole culture ecosystem with the hidden intelligence all the participants have contributed:
思路
this word means the ways one have used in thinking about the solution of a problem or puzzle. Teachers would ask students: '你解这道题的思路是什么？'(How do you solve this puzzle?) A colleague may praise your plan and initiative as "思路不错！"(Nice plan! Well thought!) This is a very commonplace word in Chinese, however it literally means 'the way of thought', English equivalent being "train of thought" or "stream of thought" or "line of reasoning" or "path of reasoning". Quoting wikipedia:
The term "train of thoughts" was introduced and elaborated as early as
in 1651 by Thomas Hobbes in his Leviathan, though with a somewhat
different meaning (similar to the meaning used by the British
associationists):
By Consequence, or train of thoughts, I understand that succession of
one thought to another which is called, to distinguish it from
discourse in words, mental discourse. When a man thinketh on anything
whatsoever, his next thought after is not altogether so casual as it
seems to be. Not every thought to every thought succeeds
indifferently. — Thomas Hobbes, Leviathan, The First Part: Of Man,
Chapter III: Of the Consequence or Train of Imagination
yes, 你的思路是什么? A hidden wisdom lies deep in the language itself without being discovered before one starts to think about exactly how people would think, the succession of ideas and nodes in the neural network, and the vivid transmission of concentration from one node in the word-sense network to another, a path leading from the starting of a maze till the end of it, and a bridge linking the different aspects of existence itself and cutting through the darkness and mist of unknowness. 思路, is the exact word people could use to denote our thinking mechanism.
similar expressions are '思绪'(threads/strings of thought, similar in meaning to 思路, but stresses more on sentimental feelings or thoughts) or '思潮'(waves of thought, to describe the massive spread and expansion of thoughts within people and society)
