Welcome to DBForums!
You've got some great questions, but you really need to get at least an intro course or equivalent knowledge to be able to ask the right questions in enough detail to get the answers that you really want. I'll try to give you the 30,000 foot view, but keep in mind that as you start to understand more of the "gory details" and ask more specific questions that these answers are targeted toward a novice and you will almost certainly take issue with these answers once you learn more.
Database Modeling tends to be more toward the abstract or logical part of the design. It doesn't get down to the nitty-gritty details of how to make things work.
Database Design tends to be more toward the physical implementation. Which size and type of integer does this particular attribute need to use. Which type of disk does this part of the database need to use (the choice between SSD, premium QOS, bulk storage QOS, etc).
I really doubt that you can get a job based on a single course. Most junior colleges offer 18 to 36 month programs to get you enough education to be able to start working in the field. Most universities seem to expect a Masters Degree for database professionals, although they tend to place graduates in a completely different environment (not just at a higher level in the IT field, but in a differnt part of the field).
One thing that you'll find very quickly is that if you want to stay current in IT, school is simply part of the "ante" to get into the game... Your learning/training will never stop as long as you want to stay even semi-current.
In theory, theory and practice are identical. In practice, theory and practice are unrelated.