In many textbooks, polite style speech is taught, which means です and ます endings are introduced, and used in many sentences.
However, I have encountered sentences with omissions, for example sentences which omit verbs. They may also end with particles. I think this is done to introduce vagueness, or simply to make the sentences shorter.
In what context do such omissions constitute not polite speech anymore, but plain speech? For example, in the drama Meguri Ai, Episode 8, there are some "incomplete sentences" that have differing levels of politeness (I have some context and sentences written here, but if more background is desired, the specific video segments are listed below - please visit https://youtu.be/mNOOEfpjuUM):
Video time: 02:35 - 03:30:
A boss (社長, name 修二) is in the back of a taxi with his subordinate (社員), and the subordinate says this to the driver. Although polite forms were used with the driver up until that sentence, I feel that this sentence is in plain form as the subordinate feels superior to the driver due to a perceived difference in social status.
Video time: 11:25 - 11:45:
Apparently this sentence is still polite, according to my teacher. I am not sure why, though.
Video time: 12:53 - 13:10:
Eri (絵里) asks どうして, which apparently is in plain style, and Shuuji (修二) replies in plain form with two occurrences of から without です.
There are many sources that state that ending with から is informal. However, まで is another particle, yet ending with まで without です (second bolded sentence) seems to leave the polite style speech unaffected. Again, どうして without です seems to be informal.
When does omission make sentences casual / plain? Examples would be greatly appreciated.