Using a "colon" after "is" or "this"

Referring specifically to The Chicago Manual of Style (17th ed.), 6.64, it says this:

6.64: Colons with “as follows” and other introductory phrases

A colon is normally used after as follows, the following, and similar expressions.

      The steps are as follows: first, make grooves for the seeds; second, sprinkle the seeds; third, push the earth back over the grooves; fourth, water generously.

      Kenzie’s results yield the following hypotheses: First, . . . Second, . . . Third, . . .

On the other hand, a colon is not normally used after namely, for example, and similar expressions; these are usually followed by a comma instead.

This would be a specific exception to the general guidance that what precedes the colon must stand on its own as an independent clause.

While Chicago is only one of many guides, and different people follow different styles (so, this is matter of opinion), if we are to follow Chicago guidance specifically, it's likely that all of the example sentences would be rephrased.

Here are some variations, each starting with a version that doesn't use a colon.

1. a) My next wish is to bring my father back.
1. b) My next wish is as follows: to bring my father back.
1. c) My next wish is the following: to bring my father back.

2. a) Consider that I am the king of this castle.
2. b) Consider the following: I am the king of this castle.

3. b) The real question is if you are a man or a mouse.
3. a) The real question is as follows: Are you a man or a mouse?
3. b) The real question is the following: Are you a man or a mouse?

Note that I followed Chicago (6.63), when deciding if the first word following the colon should be in lowercase or capitalized:

When a colon is used within a sentence . . . the first word following the colon is lowercased unless it is a proper noun. When a colon introduces two or more sentences . . . or when it introduces speech in dialogue or a quotation or question, the first word following it is capitalized.

In your first example, I can't see that punctuation is needed at all. "To bring my father back" isn't a clause because it lacks a finite verb and, although the first part, "My next wish is", does have a subject and a verb, it seems too truncated to qualify properly as a clause, dependent or not. If you switched the two parts around, thus: "To bring my father back is my next wish" you can see that what's happened is that one independent clause has been artificially cut into two. "To bring my father back" is the subject of the finite verb 'is' and "my next wish" is the subject complement. In the next two examples, I think the colon is acceptable if you take the view that quotation marks around "I am the king of this castle" are implied, and that the question mark at the end of the third example doesn't apply to the whole sentence so there has to be a clear separation between the first part of the sentence and the second.