Updating Theme

Hi, I have a very newbie question, although I am not a newbie and should know better. I have, for years, used the theme pressplay, which is no longer even being updated. Nonetheless, it has worked for my site and there are so many other things I need to do on the site, I have not changed it. I created a pressplay child theme which I have been using for a long while, although the only thing in the child theme folder is a css style file. So, I have two questions:
1. Do I need to add any other files to the child theme? Like function.php? And if so, how?

2. Once the child theme is good, if I update the parent theme will the child theme just roll on top of it? I guess what I mean is, what if the parent theme updates function.php, but it is in my child theme? Do I then need to manually go and apply my little changes to the new, updated theme?

Sorry, I feel a little bit out of it on this, so thanks in advance for any help you can give.
Debbie

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