Creating one keyframe altered the position of the character in all remaining frames??

This is my first time trying 3D animation. First week and a half with blender with no prior experience with 3D model or animation. Only experience is watching cartoons for enjoyment as a kid and as an adult. First week I solely looked at modeling tutorials. A light bulb turned on this afternoon. If my focus is on 3D animation, maybe I should simply dive into animation head first. There are so many already well made rigged character models on the net that I can use to hone in my animation skills following the 12 principles of animation.

Character model from this link.

Two Part Question:

(1) Somehow manipulating the character model for one frame completely altered the position of the character in all the remaining frames. Trying to make the character jump, instead of puling the “blue” (Z axis) arrow, I decided to highlight the entire character model (using “B” command and marque selecting the entire model), and pressed “G” to move the character up, resulting in the character now hovering a few feet off the original ground/base in all frames.

Note: I was able to fix it in one frame, but that would be time consuming. I manage to get her back on the ground by revisiting a random frame, pressing “G” and moving the character back to the yellow line/ground, then pressing “I” to insert frame. However, all the other 20 frames or whatever number of frames still has the character hovering above the yellow line. I tried selecting all frames (pressing “A”) within the dopesheet, and moving the character, but immediately checking each frame, the character is back hovering.

(2) How do I select the character in its entirety if the character comes rigged with separate arms, clothes, head, face, etc, especially if there is another character within the same scene (I had to “append” the second character into the scene; found this from youtubing because I wanted two characters in from different blend files).

Using “B” marquee selecting tool command will obviously work, but it’s not going to work if I have both characters tangled together dancing or something.