1. First answer from a teacher:
   https://jakubmarian.com/so-thus-therefore-and-hence-in-english/
   "So, thus, therefore, and hence in English"
   Since you are reading this article in English,
   the odds are you already know what the conjunction "so" means.
   You probably also know that "thus", "therefore", and "hence" mean basically the same as "so", and you are wondering what the difference is. If this is the case, this article is just for you.

Before moving on to the particular words, it should be noted that:

• "thus", "therefore", and "hence" are all rather formal and much more common in writing than in everyday conversation.
• where they are almost always substituted by "so".

“Thus” and “so”

The most important difference between “thus” and “so” is that:

• "so" is a conjunction(meaning "and for that reason", "and because of that"),
• whereas "thus" is an adverb(synonymous with "consequently").

For example, the sentence

He is not satisfied, so we must prepare a new proposal.
can be rewritten using "thus" as follows:
correct
He is not satisfied. Thus, we must prepare a new proposal.
He is not satisfied; thus, we must prepare a new proposal.
He is not satisfied, and(,) thus(,) we must prepare a new proposal.

wrong
He is not satisfied with it, thus we must prepare a new proposal.

"Thus" is usually separated from the rest of the sentence by commas, but the commas are often omitted if this would lead to three commas in a row (as in the third example).

The last example is not correct because "thus" cannot join two independent clauses.

"Thus" also has another meaning: "in this way", "like this"(in which case it does not introduce a clause). For example:

They have developed a new technology, thus allowing them to reduce costs.
The comma here was appropriate because what follows "thus" is not a clause. It is just a parenthetical expression extending the preceding clause.

"Hence"

Just like "thus", "hence" is an adverb, not a conjunction,
so it cannot join two independent clauses(note that it is more common to omit the commas around “hence” than after “thus” in formal writing):

correct
He is not satisfied. Hence(,) we must prepare a new proposal.
He is not satisfied; hence(,) we must prepare a new proposal.

wrong
He is not satisfied, hence we must prepare a new proposal.

“Hence” used in this sense is rather uncommon, and such usage persists mostly in specialized fields, such as scientific writing.

There is, however, another, more common meaning of “hence”, which substitutes a verb but is not a clause in itself and is always separated from the rest of the sentence by a comma:

Our server was down, hence the delay in responding.
The chemicals cause the rain to become acidic, hence the term “acid rain”.
As you can see, “hence” substitutes phrases such as “which leads to” or “which is the reason of”.

Second Answer:

Usage of "So", "Therefore", "Thus", and "Hence"
As a native speaker, I would break it down as follows:

1. So: This option is the most informal, and what you would use in conversation. "I worked very hard, so I am really tired."

2. Therefore: This is a little more complex from my perspective. Here you are using 'thus' to mean 'as a result of'. It can be seen as somewhat archaic (old fashioned), and it would be uncommon in casual conversation. It would be more commonly used to indicate that is happened in the past, but can be used in the way you are describing. "Yesterday I worked really hard, thus (as a result of working so hard) I was tired." But again, unusual in casual conversation, where you would usually use 1.

3. Thus is again possible to use in that context, but is more commonly seen in logical reasoning. "A is B. B is C. Therefore, A is C."

4. Hence is similar to 2, and can be used, but is usually in the context of future events rather than past events.

In all your examples, there are no rules against usin