1. He said, "The boy broke the window."

2. He said that the boy broke the window.
3. He said that the boy had broken the window.
[Which one is the same as #1? Is it #3? What about #2?]

4. He said, "World War I broke out in 1914."
5. He said that World War I broke out in 1914.
6. He said that World War I had broken out in 1914.
[Which one is the same as #4? Is it #5? What do you think about #6?]

Yes, 1 and 3 mean the same thing, although in today's casual speech, either 2 or 3 would be taken as correct.

And 5 and 6 mean the same as 4, even though 6 uses verb tenses correctly and 5 is a bit off.

Regarding the first set of sentences:

1. "He said, 'The boy broke the window'" is a direct quotation where the speaker is reporting what someone said exactly as it was spoken.
2. "He said that the boy broke the window" is an indirect quotation where the speaker is reporting what someone said but not necessarily using the exact words.
3. "He said that the boy had broken the window" is an indirect quotation in the past perfect tense where the speaker is reporting what someone said but also indicating that the action of breaking the window had already occurred before the reported speech.

So, you are correct that #3 is the same as #1 because it maintains the same tense and accurately reports the speech in an indirect manner. On the other hand, #2 is not the same as #1 as it uses a different tense (past simple instead of present simple).

Now, moving on to the second set of sentences:
4. "He said, 'World War I broke out in 1914'" is a direct quotation where the speaker is reporting what someone said exactly as it was spoken.
5. "He said that World War I broke out in 1914" is an indirect quotation where the speaker is reporting what someone said but not necessarily using the exact words.
6. "He said that World War I had broken out in 1914" is an indirect quotation in the past perfect tense where the speaker is reporting what someone said but also indicating that the action of World War I breaking out had already occurred before the reported speech.

In this case, #5 is the same as #4 because it maintains the same tense and accurately reports the speech in an indirect manner. However, #6 is not the same as #4 as it uses a different tense (past perfect instead of past simple).

To sum up, #3 is the same as #1, and #5 is the same as #4, while #2 and #6 differ from their respective original sentences.