Learn English – Punctuation to introduce a list: comma vs. colon vs. nothing

In your example, the first one is correct but the second one is incorrect.

Use a semi-colon to connect two related independent clauses.

They took the money from the vault; they took it quickly.

The ideas are related, the clauses stand on their own, semi-colon is OK here.

Use a colon to separate equal things (like an '=' sign).

Just remember three things: be on time, bring the money, and come alone.

The things here = those three items.

The Chicago Manual of Style, 14th Edition, section 5.97 agrees with you that a colon is used

to indicate a sequence in thought between two clauses that form a single sentence or to separate one clause from a second clause that contains an illustration or amplification of the first[.]

It also notes, however, that

In contemporary usage [...] such clauses are frequently separated by a semicolon [...] or are treated as separate sentences[.]

I personally would go for a semicolon in your 4th and 5th examples, and a full stop in the last, but the colon is certainly a viable choice.

(Section 5.99 also agrees with you that a colon is absolutely the correct punctuation to introduce an otherwise unadorned list as in your examples 1 and 2.)