見たければ見なさい = もし、あなたが見たければ、「（あなたが）見なさい」と私は許可します（私は命令します）。
is correct although the target of the observation is the subject of the main clause (like in sentence 5). Could you explain why this sentence is correct and sentence 5 is wrong?
Who is the observer of the conditional clause "（あなたが）見たければ(If you'd like to see it.)" ?
Strictly speaking, I(私) don't care whether you(あなた） want to see it or not. On the other hand, you know (=you off course can observe whether you want to do or not.)
Then the observer of this conditional clause is "you".
Main clause of this sentence is an imperative sentence, so the subject of main clause is "私(I)."
Thus the subject of conditional clause and main clause are different.
Sentence 2 (in my question), as you have said, is okay. However the sentence with 彼女が希望すれば、彼女は。。。つもりです may sound unnatural for a different reason, that つもり isn't really used for other people. So I am not totally convinced that it is unnatural because of a wrong use of ば... What do you think of sentences 3 and 4 in my question, which use 私。。。つもりです。
2 State verb + different subjects
I observe whether she wants to marry me or not, and if I get to be aware that she wants to marry me, then I'll marry her.
This sentence is natural.
However the following is unnatural.
This is unnatural.
If the sentence is "彼女は私と結婚するつもりです。そのように彼女は希望しています。", then this sentence is natural.
In short, the main clause "彼女は私と結婚するつもりだ" depends on the conditional clause "彼女が希望すれば". If the conditional clause"彼女が希望すれば" is true, then the main clause "彼女は私と結婚するつもりだ" get to be active (by the subject of the main clause.)
So If you can control whether the conditional clause gets to be true or not, "if-then" sentence doesn't make sense.
I'm now aware that this matter doesn't only depend on the grammar but the meaning (whether it make sense or not).
3 State verb + same subject
(私が)卒業できれば、(私が)彼女と結婚するつもりです。=私が卒業できれば、私は彼女と結婚します。 In this context, "結婚するつもりです" is equal to "結婚します," even "結婚します" shows strong will than "結婚するつもりです。"
4 Action verb + different subjects
I have never been a Japanese language teacher but I've been an engineer for forty years. I analyzed this issue as the following way.
The sentence No5 is somewhat unnatural.
5 田中: 山下さんが来られれば、(山下さんが)知らせてください
5-improved, natural 田中:山下さんが来られるのであれば、（山下さんが）私に知らせてください。
So we have to focus on the phrase "山下さんが来られれば.=山下さんが来られる(action)のであれば、or 山下さんが来られた(state)のであれば"
"山下さんが来られる(action)のであれば"="If 山下さん comes here", "（山下さんが）私に知らせてください。" = "let me know it" is natural.
I think there could be the following rule.
- The observer of the conditional clause is A.
- The subject of the conditional clause is B.
- The verb of the conditional clause is a state verb. (Thus the observer is necessary.)
- The subject of the main clause is A.
- If the subject of the main clause (A) is equal to the subject of the conditional clause (B), the sentence is unnatural, wrong.
彼女(B)が希望すれば(the observer of this conditional clause is 私(A))、私(A)は彼女と結婚するつもりです。
This sentence is OK.
彼女(B)が希望すれば(the observer of this conditional clause is A)、彼女(B)は私（A)と結婚するつもりです。
This sentence is unnatural and terrible!
5 "山下さんが来られれば(山下さんが)知らせてください" is unnatural or wrong.
"山下さんが来られれば" The subject of this conditional clause is 山下さん, and the observer of this conditional clause is 田中 (not 山下さん who is the terget of this observation.)、
"来られれば" is somewhat ambiguous, but if a reader feels that it means "come into the picture" or "appear on the scene," then it is semantically the state verb.
Then here the target of A's observation (or the subject of condition clause with state verb) is the subject of main clause, it's unnatural (or wrong).
"(山下さんが)知らせてください。" ="Hey Mr.Yamashita! Let me know it!"
The (semantical) subject of main clause is 山下さん.
Then totally No.5 is unnatural.
6 田中: 山下さんが来られれば(竹内さんが)知らせてください
For me, this one is OK.
It can be improved as the following.