I am from London. I would always use the linking /r/ in general conversation when there is no reason to pause, including in all the examples you have given. I don't think this rule is variable.
Perhaps I might add pauses if I wanted to enunciate something particularly clearly e.g. if there was a communication problem or in a very formal presentation to a large group of people. The loss of the linking sound would happen because of extra pauses between words. If one dropped linking /r/s, one would usually sound false and unnatural.
The answer is yes to all three. Michael summed it up nicely. When I speak at normal speed 'for' gets reduced to fə/.
I'm certainly not an expert on non-rhotic Southern accents, but the following should work for intervocalic silent R:
Paragraph, current, curable, incorrigible, marathon, Carolina.