The posts column number means "they make this many posts and they get upgraded"; you'll want to reset Users back to the 0 it was by default, unless you plan to have it set that users are in a temporary group until they hit a specified amount of posts.
If you wanted to make that First 100 group be where people go after making 100 posts, you'd put 100 in the posts column.
As for adding a new group and existing ones being cleared out, the create group routine is extremely basic, there isn't anything in there that would change any existing groups, feel free to take a look at /admin/docreategroup.php; the only thing I can think of is if the auto group assignment of "1 post" in the users group could be throwing things off.
Okay not knowing how you add groups. Or at least add members to a new group. There is a field on the main group screen. called posts. It is for auto promote to a group after x many posts The disabled ones should be zero."0" You have several that are null. According to your screenshot. Plus users set to a 1 post. I would set them all to a "0" if it were me.
Is not the users group your default registration group? If you allow guests to post they auto promote to a user group after one post. Even if they don't register.
If you don't desire a auto promote. Maybe when you create a group it is adding them without your intervention if it does not have a zero in that field..
But in any case it has always been when adding a member to a new group that they elect to use the new group image. It should not delete the existing group images they have already. And there has never been any notification that they have a new image to use. Now if you change an existing image that works without a member intervention..
The problem is when I create a new group, all group images get reset from all my users that chose to display what they wanted and they'd need to go back into editing their profile to display what they want again... There group image setting gets reset as a result of creating a new group.
Upon adding a new Group with a new Group Image, I noticed that users who had an image set before the change, would end up losing what they had saved for their profile and had to re-apply their group image(s)... Could this be fixed or is this just something unavoidable? I'm using the Group function as a way for my users to earn new "badges" (Group Images) for special events and eventually, competitions. The concept is, if they win a competition, they'll be added to a group with a new image (badge) for their profile.
I think it's a great rewarding system... i.e. What I've got going on now is, the first 100 registered users receive a badge (image) because they've been added into a custom group that's only for the first 100 registered users... and for December, active users in the month receive a limited edition 2017 Holiday Tree... lol. Anyways, I hope creating further new groups can somehow stop resetting what users have chosen to display on their profile...