If there is more than one part to a time phrase (e.g. both 今天 and 八点) can I place one of them before the subject and one after? Is there any situation in which this would be okay?
他今天八点要去看电影 (not split)
vs.
今天他八点要去看电影 (split)
On a similar note, if there is both a time expression and another adverb, can I split those up?
电影六点就开始了 (not split)
vs.
六点电影就开始了 (split)
Yes you can, when you split it like that, you emphasize the time, when your friend run out of the time, you can use it to push them.
see Chinese grammars, e.g. Adverbial Phrase Placements in L1-Chinese ESL Learners' Writing https://pdfs.semanticscholar.org/4bf3/7bd9e7a58932a498e25da9402305ab4c7e4d.pdf Punctual time adverbs may be positioned before the main verb as shown in (2) or they can move to the beginning of a sentence, before the subject of the verb, as shown in (2a) 明天我要去公园。
＂汉语语法基础＂ ３。２０ 状语的位置 句间定语的位置只有一个：主语之后，中心语之前，要紧接着中心语。因此定语就没有必要单讲它在句子里的位置。状语的情况与此不同。它也必须位于中心语之前---这一点跟定语相同，却不一定要位于主语之后--- 这一点跟定语不同。位于主语之后的状语是一般的情况，不需要再谈；位于主语之前的状语，可以叫作句首状语，需要谈一谈。１。表示时间的名词或者方位结构可以作句首状语。例：（１）今天我想讲一点关于我们的党的作风问题。（毛泽东，整顿党的作风）（２）现在我们的党还有什么问题呢？（同上）（３）五四运动时期，一般新人物反对文言文，提倡白话文，反对旧教条，提倡科学和民主，这些都是很对的。（毛泽东，反对党八股）（４）抗日战争爆发以后，革命的文艺工作者来到延安和各个抗日根据地的多起来了。（毛泽东，在延安文艺座谈会上的讲话）
表示处所的名词或者方位结构这种可能就比较少，＂屋里坐着一个人＂之类的句子是无主语，状语尽管在一句之首，但是根本安不上主语，跟这里谈的性质不同；而＂咱们北京见！＂虽然有了主语却又不大好提在主语之前说成＂北京咱们见！＂ II。一部分副词可以作句首状语。如：（５）刚才凯丰同志讲了今天开会的宗旨。（毛泽东，反对党八股）（６）难道我们还欢迎任何政治的灰尘、政治的微生物来玷污我们的清洁的面貌和侵蚀我们的健全的机体？（毛泽东，论联合政府）（７）忽然她浑身一跳，就扑到床上，从破棉絮堆里抱过那不满半岁的孩子。（茅盾，当铺前）（８）幸亏荐头（employment agent (arch.)job broker）的情面大，辞退不得，便改为专管温酒的一种无聊的职务了。（鲁迅，孔乙己） 能够作句首状语的副词不太多。有些句首状语不宜于放在主语之后，如果放在主语之后，意思就有所改变，例如（８）的＂幸亏＂。试比较：幸亏他来了。--- 他幸亏来了。＂幸亏＂作句首状语，＂有幸＂的不是主语，而是主语以外的人。＂幸亏＂作句间状语，则＂有幸＂的就是主语。
Since different types of adverbials, see e.g.this site, The word order of co-existing adverbs in a sentence can be split by the subject with time adverbial occurring before the subject,it seems that time adverbial adjuncts consisting of 2 parts can be split by the subject (and be justified by belated realization of need for more precise statement) although this splitting seems uncommon, in other words it seems hard to find examples on the web.
Although both versions native speakers can understand, we use the "non-split" version (the first sentence) more often. I think it's because the subject (主詞) is usually the first word.
The standard word order is Subject Adverb Verb Object. Time adverbs are much more fluid in positioning than place adverbs, i.e., can do S time-adverb V O, or time-adv S V O.
The difference is what I call "focus" (I distinguish between "focus" and "emphasis", as there are emphasis words, e.g., 并 to go with 不, emphasizing the negative).
他今天八点要去看电影: sentence starts with 他, so the focus is on 他 (not 我, not 你), i.e., What's he going to do?
今天他八点要去看电影: sentence starts with 今天, so the focus is on 今天 (not yesterday, not tomorrow), i.e., "What's happening today? He is going to see a film at 8 o'clock" (whereas I'm going to do something else, say; implied, not necessarily overt contrast).
Ditto with: 电影六点就开始了: sentence starts with 电影, so focus is on 电影. 六点电影就开始了: sentence starts with 六点, so focus is on 六点.
It's what I call (in my teaching) the linguistic flagging up equivalent of physically holding up 1 of, say, 3 objects. All eyes will look at the object held up, so when you say, "It is...", they know which of the 3 objects "it" refers to. So when you start with 今天, they'll focus on 今天, not 昨天 or 明天. When you start with 他, they'll focus on 他, not 我, not 你.
My gut feeling is:
“今天他八点” emphasizes the condition of "今天". “六点电影就开始了” emphasizes “六点”.
But my second thought is:
Even when i want to emphasize “今天” or "六点"，i may still use “他今天八点” and "电影六点就" sometimes.
Yes you can, if you want to shift the focus, and you know exactly why you're doing it
他今天八点要去看电影 = he's gonna do something sometime today
今天他八点要去看电影 = Today, he's gonna do something, (and tomorrow, he's gonna...)
For example, is he free today?
Oh today he's gonna do something at 8pm
But it's not a common phrasing
电影六点就开始了 = The movie starts at 6pm
六点电影就开始了 = 6pm is when the movie will start
