I read a page on Russian Impersonal constructions a few days ago by the RLM. It was all about impersonal constructions. But, it's just not clicking for me. For example: "Пашу тошнило всю дорогу". Why does this sentence govern the neuter form of the verb? Another question I have is with this example: "Едва самолёт взлетел, как один из моторов заело." Why does this also govern neuter form of the verb? I was taught earlier that impersonal construction use dative case, and these use accusative case? Please explain how to form impersonal constructions.
Пашу тошнило всю дорогу.
The impersonal neuter verbs + Accusative case in the constructions like this are often used to show conditions or feelings. The typical dummy subject 'it' is omitted here, but still the verb agrees with 'it', this is why it is neuter: тошнило (a verb describing one's condition - being sick)
Едва самолёт взлетел, как один из моторов заело.
Here you have the dummy subject 'it' omitted again. It is an impersonal construction describing the condition of the engine (broken).
The usage of the impersonal construction rather than normal active voice sentences can be explained by the topical analysis. Since Russian is a topic-prominent language, i.e. syntax follows the topic (what's new is in your message), not the straight S-V-O logic, those impersonal sentences shows what exactly you wanted to say, highlighted the new part of the message. You can read more about topic-prominent languages here.
I'm not sure, but I think, neuter form of verb in cases like this are used for something like passive voice. Compare following:
Пашу всю дорогу тошнило
Паша всю дорогу читал
один из моторов заело
один из моторов сломался