Finally got a job, and question about EAD

After three months of sending out countless number of resume, being asked by stupid recruiters about the details of my EAD, I got an offer as a developer in a big Financial company. I think their professionalism prevent the HR from asking too many questions for their candidates (the law prevent them from asking too much, but somehow lots of small companies ask anyway).
during the onsite interview with the HR, she only asked 2 questions regarding my working status :
1: Are you legal to work in US? I said Yes
2: Do you need sponsorship? I said No

Now, I am wondering, do most of the type of EAD require sponsorship after it expired?
Because clearly our EAD cannot be sponsored anyway. I am hoping the HR will not make a wrong assumption that I am a greencard holder/citizen. Whats your opinion about this? DId I answer the questions correctly and precisely?
Btw, this company hires lots of international students as well. Therefore I think even after they know I am EAD holder it wouldn't cause any problem. I am afraid because apparently my salary is way higher than most of the international students graduates I know, I think internally there may exist a salary difference between international students and "local" students because the company has to spent $$ and time for their greencard sponsorship

Green card holders or citizens do not use EADs.

I know that. And?

They can't assume you're a GC or USC. EADs are only given to foreigners. Most do not require sponsorship. You answered everything correctly, it's cool.

And I presume that 1) is supposed to say legal, not illegal in your post

Oops......sorry I updated it

Good to hear!

1. They're asking you if you need "H1B work visa" sponsorship. You don't need that.

2. If you are grandfathered under 245i, you can ask them to sponsor them for greencard.

If Dream Act passes however, you wouldn't need them to sponsor you for greencard. Dream Act will put you through the process of greencard without their help.

After few months of experience, I advised DACA applicants with advance degree go apply for big company, I think big companies are good for freshgrad and the interview and applying process really make us feel much more comfortable and respectful from the employer.

Don't worry about it. You will be asked to fill out a form on your first day of work that has implications on when your work eligibility ends. HR will then bug you 3 months before it does and remind you to update your status.