Your quite ok to give cj your ssn, its not all defcon 1 to do so in this case. cj has required it for years now. All you need to worry about is filling out a w9 form they send you and your 1099 form they send you if you make over $600 in a physical year. The w9 is a standard contractors form (you in this case not directly working for cj, but as freelance contract). It allows cj to report to the irs that they paid you, and if and how much taxes you charged cj for your work. it allows them to request and use your ssn. The 1099 form is also like the w9 but lets the irs tax you correctly in your respected tax bracket, cj by law has to report what they paid you, this is so you cant lie how much you actually made and scam the government. These are standard forms.
I know in Canada, once you get your sin #(ssn in your case) you need to file taxes even if your income is 0. in your case it may differ, but your tax name is your name on your ssn card , full birth name usually . Your income will be 0 if you dint work, you dont need a passive income for cj, something you made up with wrong understanding of the process.
As for employer id, I know in Canada its a gst/hst number, but thats when your making over 30k.. You need to call the irs general inquiry line , they are friendly , and will answer this question how to get one or when you need to.
Remember, your self employed , you dont need to register a business # or llc until your making alot more, wanting to hire staff , or want to write off bigger business expenses . sole proprietor (contractor ) is just your name, no extra, and you can still file work expenses at the end of the year to get more money back , and pay less taxes. find an accountant 2 months before tax season, should cost about 150-200 for your personal, self employment and expense report to be filed . Your accountant will deal with all that, just save all your paystubs and recipts and plop them on his desk.