I don't see a real issue either way. Technically, employment is not the same as a student. However, do what makes you more comfortable since it is not a red flag at this pont.
No. That is not correct.
1. I-130 is processed by USCIS. (can take a year)
2. I-130 is sent to NVC.
3. NVC requests documents and fees
4. After document qualified, NVC sends case to consulate in home country. (after case is at front of the line)
5. Consulate interviews applicant.
6. Consulate issues visa
7. Visa holder travels to US.
The entire process can take 2 years.
You don't have to have a W-2 to report income on a tax form. You simply list it. However, to prove annual income for immigration purposes, you will need an employment letter, etc.