I am not aware of any generally accepted meaning for two dots. As you say, one dot is a period, which marks the end of a sentence or an abbreviation, and three dots is an ellipsis, which indicates that text has been omitted, or a long pause in speech. But two dots has no specific meaning.
If you saw two dots somewhere, my guess is that it's a typo: The ...
There are several different ways of mentioning the three things.
A direct parallel to the first example sentence in the question is actually different from the second example sentence:
One thing is A, another is B, and the third is C.
Alternatively, you can introduce the list items with a colon or dash:
There are three things: A, B, and C.
There are three ...
Rather than "independent clause" I'd describe these as two coordinated clauses:
you have a good time with her
everything is going according to your plans
They are equal to each other and joined with the coordinating conjuction "and".
A comma is correct, but I'd consider it optional, as both expressions are subordinate to the "I ...
 John slipped in front of the bank, [which was embarrassing].
 You have to write a thesis in the end, [which is a cumbersome and lengthy process].
It's not "which" that is the relative clause, but the whole bracketed elements.
The relatives here are clearly non-restrictive; they simply provided non-integrated content that is not required to ...
If the job involves cleaning every day, I would call it a "cleaning job". "Job" in this case is similar to "occupation" or "regular employment".
If by "job" you are referring to a single occasion, then "cleaning-up job" sounds just fine to me - written with a hyphen. It is an attributative noun, ...