The present perfect continuous is, in most cases, used to describe an action that is ongoing:
I have been pumping
means: "I have pumped, but I'm not done yet; I'm still pumping."
By contrast, the present perfect is used to describe an action that has ended:
I have pulled up dandelions all day
means: "I've spent all day pulling up dandelions, but now the day is done, and my task is over."
For almost all of the sentences you give, I could imagine different contexts in which one of the two choices would be acceptable. It all depends on the context.
That said, I would favour the following:
I have pumped up three tyres. Would you like to do the fourth?
The latter question seems to imply that the first three tyres are now properly pumped up. Now, someone has to pump the fourth one up.
She has been polishing this table all morning and she is not satisfied with it yet.
The fact that she is not yet satisfied with it yet seems to imply that she is still working on it. The task is ongoing; therefore, the present perfect continuous should be used.
I only have heard about him twice since he went away.
The use of "only" here implies that the present perfect must be used rather than the present perfect continuous.
He has been riding, that's why he is wearing breeches.
He's still wearing breeches, which may imply that he's not done riding.
I have been hearing from her regularly. She is a very good correspondent.
That last statement indicates that communication with her has not stopped, but is ongoing; therefore, use the present perfect continuous.
EDIT: However, there are exceptions. The present perfect continuous does not always describe an action that is ongoing. Here is an example:
I can smell whisky on your breath! Have you been drinking?
Here, when the question is asked, the drinking has presumably already come to an end.