Proper way to make a tweaked theme into child-theme setting?

As said, it is bad practice to make modifications to any theme/plugin you are not the author of, the simple reason been, if you ever update that theme/plugin, all chnages will be lost. You should always create a child theme or a functionality plugin

You said that you cannot get the parent’s stylesheet. There are two thing to have a look at that is very important in your child’s stylesheet. One is the template path and the other the @import part. The template path should be the name of the actual folder in which the parent’s stylesheet (style.css) is in, and the @import part should be the actual path to the parent style.css. Here is an example of a twenty fourteen child theme taken from the codex

/*
 Theme Name:   Twenty Fourteen Child
 Theme URI:    http://example.com/twenty-fourteen-child/
 Description:  Twenty Fourteen Child Theme
 Author:       John Doe
 Author URI:   http://example.com
 Template:     twentyfourteen
 Version:      1.0.0
 Tags:         light, dark, two-columns, right-sidebar, responsive-layout, accessibility-ready
 Text Domain:  twenty-fourteen-child
*/

  @import url("../twentyfourteen/style.css");

To come back to your other quesation, the best way to work around your problem is to have a copy of the unchanged parent theme and the modified theme next to each other, and work through each template, and transferring each diffirence to a child theme. Painful but worthwhile at the end.

From your comments, you can simply just copy everything over to a child theme for a quick fix, but this will bloat your child theme a bit. One thing to keep in mind, any function or functions.php cannot just be copied to the child, it will trigger a fatal error. Here you will have to just copy the changes