Purpose of 着 in this:
管 着 男孩
Action in progress, in the past in this case.
女孩总是像姐姐一样管着男孩，男孩也非常愿意让她管。
The girl was always looking after the boy like an elder sister, and the boy was very much willing to let her.
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so would the construction 像。。。一样 just mean ‘like…’?
Yes.