I'll break up your post and reply to each point in turn!
I wrote rule 4 & combined inference from rule 3 as:
T NOT in 1 (this means T is in 7 because of rule 3) Rule in 1
CP: R not in 1 (R open to go anywhere else) T in 1
That is absolutely correct.
For this reason, I understood that the answer choice to rule sub. question had to have the same effects as T being in either 1 or 7.
This is already a bit of an issue - what you're saying here is the 3rd rule. We're substituting for the 4th rule. The 3rd rule will always be in play anyway, so there's no need to substitute for it or to choose an answer that has the same effect as it. Any answer we pick will always be subject to the 3rd rule, which we can still use, so this is not a useful way to evaluate answers.
With this analysis, I had (C) & (D) as answer contenders:
(C) Diagrammed: R NOT 7 (R open to go anywhere else) T in 7.
CP: T NOT IN 7 (this means T is in 1 because of rule 3) R in 7
This forces T to be in 1 or 7.
As before, you're evaluating the answer by whether it puts T in 1 or 7. That's not the rule we're trying to replace. For a specific problem with this answer, note that when R is not 7, T certainly doesn't have to be 7. T could be 1, with R anywhere else! Answer choice (C) forces T to be 7 anytime R isn't, which isn't true.
(D) T IN 7 R NOT IN 7
CP: R IN 7 T NOT IN 7 (this means T is in 1 because of rule 3)
This also forces T to be in 1 or 7.
This isn't what answer choice (D) says. It's:
and the contrapositive:
That's not even true - If R is 7, T must be 1. So this isn't even a true statement.
Did I misunderstand the meaning of rule 4? I don't understand why (C) & (D) are incorrect.
Now I've dealt with that. Moving on:
I thought (E) introduced a new condition as if R isn't in 1, R can go anywhere (didn't want to make a mistaken reversal of R's limitation). What makes (E) the correct answer choice?
Nothing about answer choice (E) prevents R from going anywhere the original conditions allow. The original conditions force R to be 1 if T is not 1. So answer choice (E) is certainly true:
because if T is 7, T is not 1, so R needs to be 1. That's all to the good. What if T is not 7? The rule says nothing in that case - if T is not 7, the sufficient condition of the new rule is false, so the rule "turns off" and doesn't do anything. So R is now free to go anywhere. That's as required, so answer choice (E) is correct.