How do I answer questions regarding sponsorship on company applications?

If you had your EAD after you filed your I-485, you can just answer "no" to that question.

The answer should be no.You do not need further sponsorship once you have a conditional green card.

You can truthfully say, "No, I do not require company sponsorship" for the reasons that you have independently acquired your EAD and will independently become a Conditional Lawful Permanent Resident and then an unrestricted Lawful Permanent Resident.

You would reply "NO," you do not need sponsorship. Your EAD gives you employment authorization (and there is no need for visa sponsorship to work) and, once you become a lawful permanent resident, you also do not need a sponsorship to work.

I think you can say "no."

You do not need the sponsorship. You already have the immigrant petition (I-526) approved and, unless you have some inadmissible issues, the adjustment should be approved. Until that time, your status should be STEM OPT. After I-485 approval, you are a permanent resident.

Since you have already gotten stricter work authorization, it would appear you can safely state no. While there is possibly a remote chance you might need sponsorship if your adjustment is denied, or maybe later the I-829, you can most likely safely say "no." Saying "yes" may mean they will not hire you unless they are the type of company willing to sponsor. Many companies are not. So, unless you know about facts such as working without permission or having been out of status, you can likely say no.