Google Play Store: Can I buy apps again so they can be shared with my family's library?

The documentation establishes:

Any application or game purchased after July 2, 2016 is eligible to be added to the Family Library. If you purchased the application or game before July 2, 2016, you are eligible for Family Library if the developer has made available past purchases. You can find out if this is the case by touching Read more on the application details page.

https://support.google.com/googleplay/answer/7007852

I have applications that I bought before this deadline that I would like to share through the Library of my family. Unfortunately, when I visit the Play Store page for these applications, they offer me a Install or Uninstall button instead of To buy button.

This leads me to ask:

  • Can I buy these applications again with my main Google account so I can share them through the Family Library?

  • If I buy them with a child account linked to the family, will they be shared with the other members of our family?

[ Christmas ] Open question: Is it wrong to feel irritated because I bought all of my family's Christmas gifts and my girlfriend wants to put her name on the labels with mine?

I received gifts for my family and she did not help pay for any of them and she's putting her name on the label with mine. I understand that we are together, but she is not doing the same for me with her family and I said something and she said, will you help me buy my family's gifts? I think this is unfair and she also puts her name on my Christmas cards, but she does not put mine on her. I'm just a little irritated to pay for these gifts and she did not help me and she's making it look like she did it and I do not want my family to get something for her if she can not even get something for them. This is how I feel.