possessive + gerund without pronoun
Solution 1:
Gerunds are verbals acting as nouns to describe a state of being and doing, the concepts the root verbs go to mean. So like nouns they can have possessive determiners— a noun in possessive case (John's) or possessive adjectives (your/his). However, it's used in formal English and lends beauty to the written piece. In informal situations and common parlance, we use objective forms (nouns without apostrophe's or objective personal pronouns like ' him ' , ' us ' etc. ) So first two sets of alternatives are equally correct.
In the last set of examples the same thing is told the other way round and equally hold water.
However gerunds are look-alikes of participle adjectives. We must be on our guards so that the intended meaning doesn't gather radical overhaul. Consider, for example the following sentence.
★ Whitaker did not like the woman's ( woman ) standing in front of him at the parade.
With " 's ", it is a particular instance of an identified woman ( gerundial use ) where as without " 's " it's a generalisation where the act itself is not liked by Whitaker (participal use ).