I'll answer your questions in order as able.
(1) In a warmer climate, the blood vessels near the skin tend to dilate. The dilation will tend to mildly lower BP and mildly raise HR. The HR elevation will particularly occur if a person becomes somewhat dehydrated.
(2) My best guess is that your HR lowers after a swim because you are more relaxed.
(3) There is a definite link between HR and BP. As the BP goes down, say from mild dehydration or vasodilation, the HR will increase to maintain proper perfusion pressure.
(4) I have never heard any discussion of this topic.
(5) A few not-so-well-conducted trials have examined this question: hypochondriasis and "heart neurosis" were not associated with increased cardiac events. I should be publishing a more rigorous discussion of this topic later this year.
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