Here's how we justify using either past or present:
past - If the reporting verb is the past, then it follows that the next verb should be a past form.
present - If the reporting verb is the past, but what one is reporting is a statement of fact or truth in the present, then it makes sense to use the present after the reporting verb even if the reporting verb is a past tense verb. This doesn't always work out well, but it often does. It depends on the sentence.
Here's what I think about your example sentences:
I thought the bus leaves/left at 8. - To me, it makes sense to use either "leaves" or "left" if you are talking about a bus schedule.
I thought the guy was/is dead. - Here I would use only "was".
I thought the rule only applies to employees. - To me, it makes sense to use either "applies" or "applied".
applies: It's okay to use applies because you are referring to that which could be based on fact or the truth.
applied: It's okay to use "applied" because it is preceded by "thought", which is the reporting verb.
She said her name was Claudia. - And it is, but "was" follows "said".
She said her name is Claudia. - And it still is her name. Therefore, it makes sense to use "is".