I tried searching but found no good answer. What is the standard (Like Follow/Unfollow for Instagram) way of growing a Facebook group? I have a "target group" from where I would like to collect members to my own group?
You can create a post in your group, and then "boost it", targeting members of the community that you found (the one that is similar to your target audience) Think of your content strategy too! Your group should be bringing value to potential followers. Don't manage it with the approach to make money only - developing a proper group with quality content can help you to get organic traffic, and really interested users.
I get the feeling that Facebook ads promoting groups would result in horrible engagement ... definately over $1 / engagement. Videos by far seem to have the best engagement
I think there is only one way to promote FB groups - by inviting participants from the number of your friends (or if friends will add their friends). If you're talking exactly about groups, not pages.