- Retopology is not a new term, unless you classify any term that's been around for the last 20 years "new".
- Your screenshots don't show the topology. We need to see the wireframe to determine anything (best if the wireframe is displayed on top of the mesh, not just a wireframe view).
- What do you mean you cant texture it? What does that have to do with the topology? If you retopo you will lose your UV channels, thus you need to re-texture. You can always do a Bake to Texture technique if the silhouette shape is similar after.
Doesn't matter if you repoto automatically or manual, what matters is if its correct for your outcome. You should test it in small parts for example shoulders, hands, toes. Can you rig it, does it move correctly without skin tearing etc. You should be doing things in small steps to test your tools, test how far you can push things and when you get the result you need you can roll that out over other parts of the mesh to see if it holds up. If it doesnt, back to the drawing board.
If you want to build characters/animals etc you should understand how the joints work and build the topology to suit those joints. This takes practice, lots of it. Once you get the hang of it you will see immediately how to fix these problems before they even arise. The fact you are asking tells me you probably dont have much experience, and thats ok. But if thats the case then I suggest you spend a few months practicing and get good with rigging those joints since shoulders are different to knees, and other joints, etc. Once you get the hang of that then you can texture.
