How effectively these sentences convey your meaning will depend a lot on context. And on what variety of English you are trying to speak. (I speak North American English, but I'm not very familiar with many other dialects.)
Conjunctions combine two words of the same part of speech into one unit. Modifiers that describe every part of that unit equally, and are grammatical when applied to the unit members, may be reduced as you describe, but only if they apply unambiguously to the complete unit.
It is much more clear to refer to the total number. "The four runners, two men and two women..." or "The two runners, a man and a woman..." or "The three runners..." (you get the idea).
For your examples:
1b the two running men and women
I would not understand this and I think it sounds awkward. "Men" and "women" sound like you're referring to general categories, but that makes "two" unclear. Hopefully you would have specified earlier in your context that there are, say, two couples running, or whatever is actually happening. (It is not clear that the modifiers "two" and "running" both apply to the full combined unit.)
2a the two running man and running woman
2b the two running man and woman
"Two running man" is ungrammatical in the original, un-transformed sentence (what would "two man" mean?) So both 2a and 2b are ungrammatical to me.
3b the two running men and woman
Grammar is fine but meaning is unclear. It could have your intended meaning, but without context it would not be clear to me whether the woman was running. I would also assume that either 1) there were other men present who were not running, or 2) you had already told me they were running and you were repeating it for some kind of emphasis.
4b. I have been to China and gone shopping.
Grammatically fine, but confusing unless you include the "there".
This question reminds me of one of my favorite linguistic arguments (courtesy Mark Johnson)--even if it isn't marked in the grammar, words have conceptual categories. It is confusing, maybe ungrammatical, to join words from separate categories with a simple conjunction. To see this, note that we can say:
I broke the window with a hammer.
I broke the window with my friend Bob.
I broke the window with a hammer and my friend Bob.
...because it sounds like you used your friend as a blunt object. Typically you will want to avoid this kind of possible confusion!