#1 is most common in terms of both written and spoken English

"meet with" usually implies it was on purpose, or a scheduled meeting. - eg. "I met with the prime minister for lunch to discuss the issues with the fiscal policy" "meet" can be used for both intentional and unplanned meetings. - eg. "I met Tom Hanks once. He just happened to be sitting next to me on the airplane"

In Standard English, you would say you would put say "what the motivations WERE" as opposed to another order. Some dialects invert this order, such as with New York English where you might say "what WERE the motivations", however, since you're asking about grammar, I'm assuming you want standard grammar, in which case it would be the first example. Also you should say "who was involved". "Who" always takes a 3rd person singular form of the verb. "who does this?" "who is it?" "who was there?" unless you qualify it with another plural noun, "I want to know who those PEOPLE were"

You can say "these very books" or "this very book" but you have to say "this"/"these" and you cannot use "the" i.e. you cannot say *"the very book is". However, you can use it if it's followed by a relative clause. For example: "the very book that the authorities do not want you to read" E.g. I had been looking for the holy grail for so long. Little did I know it was located right within these very walls!

You can say it both ways and both would mean essentially the same thing. If we want to be really grammatically technical, as a native English speaker, if we envision a 'location' as a setting of something in the world, then if you say 'the location of the company is California' then it means the company is in California. However, if you say 'the location of the company is IN California' then it seems to refer to a specific section of California in which the company is located. This is to say that the sentence with 'in' is potentially more specific than the first in terms of the geographical location. HOWEVER, because of the non-specific nature of the sentence, the sentences are essentially identical. In both sentences we know that the company is somewhere in California but not exactly where, even though there speaker of the sentence might know more specific details when he says 'in' rather than when he omits the preposition. Still, I would say the vast majority of people don't think about such intricate details as this ever!

For this sentence you would want to say: "I can study at the university at any time of the day" - which means: whether it's early in the morning, the afternoon, or 1am at night, you can go to the university to study. It is open 24/7

"Very interesting" can literally mean something arouses interest. HOWEVER, it is often used by English speakers to respond in a verbally neutral way, while also slightly masking or even hinting that something is displeasing. This is more common in the UK. For example, if at work, a colleague suggests a wild unfeasible project, and then asks his other colleague "so, what do you think?" The other colleague might say "very interesting..." to ostensibly remain neutral while still signalling his displeasure, but not needing to outright reject the idea and hurt his other colleague's feelings.

Both work, but "which" sounds better. And if you're going for a more formal, less spoken, and perhaps more written feel to the language, you should also say "in which paper was first produced" or even just make it an active sentence: "Paper was first produced in China"