Fine. 120,000 new jobs are created. This does not diminish the fact that 1.4 million people lost their jobs. This is what it says in the article: " Employers added 120,000 jobs last month" Based on this wording an employer can add a job and lay off 5. If you say the employee added a new job you'd be right.
No, if an employer lays off 5 and adds 1, he has destroyed 4, not created 1. It's about net addition or substraction.
Again, do the maths, you say there are every month 1 million new unemployed, which is fair enough. I don't know where exactly you live, but 1 million is roughly a 130th of the US work force. You live in an area with 10000 people in the work force and all of a sudden 75 lose their job, and then another 75 and given that 150 people have less money to spend all of a sudden since they are unemployed, every business around them will suffer too. So by multipliers, around 600-900 people will suffer since you have to add family members dependent on the work force etc and those 150 out of work will only lead to more people getting unemployed since the US economy is pretty much dependent on consumption and so on..Now make that trend continue over 4-5 months. How, after that period, will you be able to buy groceries or anything else when roughly 20% of the inhabitants in your area are unemployed, underemployed or have no regular revenue, business will close down etc.?