The only explanation I can see for the stated behavior on your phone is that you are "pressing" the Heart Rate Tile instead of briefly "tapping" it. Indeed, a quick tap will take you to the next screen while a press will invoke the "today screen edit mode".
As far as Historical "Resting Heart Rate" data/charts, please see my post from just a few minutes ago to the post titled "Is it possible to show lifetime stats on iOS app as it shows on our web profiles?".
Sorry, I can see historical trends on my phone, I can't see it on my computer. The computer only shows a brief time trend for bpm.
The computer does show history for example on steps and sleep.
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