If they have the look and feel you want then you are on the right track.
I only have a minute or two, so a couple of quick observations:
I suspect the kids in IMG_7645.JPG are the same ones in IMG_0131-01-01-01-01-01.jpeg and IMG_0159-1-01-01.jpeg. Their skin in the 0131 and 0159 ones is much darker and more yellow. Darkness and incandescent lighting I think. If you reset white balance for the tree lights, the child’s skin becomes much closer to that in your daylight photos. The tree loses its warm yellow tone. You can have warm tree and normal skin tone by a slow-ish shutter speed and a low to medium power flash. Or, you can do two layers in your editor, one for the tree with the incandescent yellow and one with incandescent white balance to give corrected colours. Merge them using a mask. Adjust layer opacity if you want to warm the child’s skin or cool the tree a little.
Try to focus on the near eye when there is only one person in the photo. When you have a group use enough DOF to have everyone reasonably sharp.
I don’t see EXIF data. In some cases, we can tell more if the data is present. If you save instead of saving for web, the EXIF data may stay with the image.
Sometimes it can be hard. Try not to shoot up the nose.
In IMG_9458.jpg, without EXIF data I can’t see if the noise is due to processing, too high ISO, or an exposure issue. Panning very slightly left or drawing back slightly would give more of the other girl’s face, which would make the photo better in her mother’s eyes.
Got to run. Questions or rebuttal welcome. Will check back when I can and others may join in too.