Q(1/3) – [IMHO] 玩 = play, playing; 玩玩 = play around, look around, fool around, hang around.
Expressed in more formal contexts? - I doubt it you would find it in “serious” literature.

Q(2/3) – This is one way to interpret it, but definitely is not the only one!
Studying Chinese by pattern will allow one to see one branch of a very big tree; studying again you will see another; one day you will see the whole three. And if this is not enough, you should notice that Hong Kong people speak differently than people in mainland China, or people in Taiwan, not to mention the way overseas Chinese speak.
Example: in China or Taiwan – people may say到城外玩玩, (perhaps most noticeably in Beijing)
In Hong Kong – people may say 去郊外玩, 去內地玩, 去美國玩.
Another example: “to have dinner at the country side” could yield the followings
到城外去吃飯; 到城外吃飯去, 去郊外食飯(Hong Kong)
please note: “去” in the first two phrases does not mean “to go somewhere”; “到” already tells you where to go, “去” tells you why we are going!
In the third phrase, “去”=”to” which tells you both – to country side, and to eat dinner.

Q(3/3) If “B” is a verb of actions, this is generally true (but there could be exception); it may not work very well with verb of “senses, feelings” etc. At least it would not sound “Native”.
To study Chinese by pattern is fine, to communicate in Chinese by pattern is not advisable – first of all, there would be too many patterns to memorize.
And if not applied carefully, it may not sound NATIVE.