How do I answer questions about my U.S. residence status? 

For questions asking if you applied for an immigrant visa, you would answer "yes" because you have filed an I-526. After a visa becomes available, you will then apply to adjust status to a permanent resident using Form I-485, after which you will mark "yes" to questions asking if you have filed an application for U.S. permanent residence.

You should answer "yes" to any question asking if you have filed an immigrant petition or applied for lawful permanent residency. H-1B is a "dual-intent" visa category, so the existence of any immigrant petition should not pose any problem.

The answer is "yes".

You should answer yes to questions asking whether you have ever filed an immigrant petition and no to questions asking whether you have applied for US residence until you are actually eligible to file I-485 for adjustment of status in the US to a permanent resident.

You have not filed a permanent residence case. After you apply for an immigrant visa, you have filed a permanent residence case.

At this stage of your processing, you have applied for Immigrant Petition, but not yet applied for U.S. lawful permanent residence. You are at the Petition stage.

In terms of how you answer the question of whether or not "you have ever applied for U.S. Lawful Permanent Residence", it is better to err on the side of full disclosure. Technically, you have not yet applied; you have only filed your EB-5 Investor Petition on Form I-526, which is a petition to determine whether or not the investment itself qualifies under the EB-5 classification. You would be applying for U.S. residency when you filed your Application for Adjustment of Status or filed your immigrant visa petition at an American Consulate abroad when visa numbers are available. However, I think the proper answer when asked whether you have "ever applied for U.S. Lawful Permanent Residence" would be "No, but I have filed an EB-5 petition on Form I-526 in order to qualify for Lawful Permanent Residency and to apply for same once the I-526 petition is approved and visa numbers are available under the quota."

I-526 is a petition based on which one can apply for residence. If the Q is "have you applied for residence" the answer is No. If the Q is "have you or anyone else filed an immigrant petition on your behalf" the answer is Yes.

The I-526 is a request for an immigrant visa so you need to answer yes and explain you have an I-526 approval.

This should be discussed with your attorney handling your H-1. He or she should be able to fully advise you.

The answer is factual. At a given point in time you either applied for permanent residency or you did not. An I-526 is NOT an application for permanent residency. It is an immigrant visa petition that if approved, positions you to apply for permanent residency or for an immigrant visa when your turn is reached on the green card waiting list. You have "applied for permanent residency" only when you have filed an adjustment of status (I-485) application and not before. If it is asked whether or not you ever filed an immigrant visa petition (unusual) the answer in your case would be "yes".