Animated explanatory videos with vector-based characters

After Effects is designed and well-suited to creating shots; it is not a video editing application. Most of my comps are single shots or transitions between shots. Think of After Effects as your on-set camera. You line up the actors (elements in the comp) and do the blocking, set up the lighting, rehearse the scene, and then call "rolling" and "action." That's what a comp is. Then you start working on the next "shot" or scene, and when you are done, you move to an editing app, which is After Effects to make the shots and Premiere Pro to edit them, and maybe Audition to polish up the sound, and you have your movie. If you use DaVinci, it's Resolve for editing and Fusion for effects. 

While you can create a five or ten-minute movie entirely in After Effects, it will be as difficult as it would be to try and shoot a movie in one shot. 

For the style of video you shared, I would probably carefully write and plan the video, divide each section into "shots" or scenes that I want to create, then use Adobe Animate to make the animated actors for each scene and have them deliver their lines, composite backgrounds and add any graphics for the scene in After Effects, then edit the scenes into a move using Premiere Pro to finalize the timing, polish the audio, and tell the story in the most effective way possible. The difference between two people getting ready to fall in love or getting ready to fight in a two-shot scene can be changed by shifting an edit by two frames. Before the blink = falling in love, after the blink = we're going to fight.

You would not want someone to build you a house with using only a hammer. It would be a lot better if they had all the tools they needed.

Many programs create output that looks the same so unless some unique effect is used it is impossible to tell you what software was used exactly. Of the programs Adobe makes that could have been animated in After Effects, Animate, Character Animator, or even Premiere Pro, there is just no way for an external observer to be sure.

1. Assuming the audio is already done then yes, you could make them in AE alone.
2.  If the character does not move around and the camera does not change angle then it could be just a single set up so you could just be a single character rig. It depends on what you need the character to do from scene to scene. In the first video you linked to it looks like all of the scenes with the waiter writing on his pad are the same looped animation for the body with only the mouth changing.

If you aren't familiar with the process of character design and animation I'm sure some people here could recommend some resources.