Can I apply for EB-5 with a pending asylum application?

Yes you can if you can meet the EB-5 requirements.

You can apply if you can show the money was earned while you have work permission. Also, unless you have valid nonimmigrant status you will not be able to adjust status and will have to leave to apply for your green card at a consulate abroad. Therefore you must not have any unlawful presence because if you have over 180 days of unlawful presence, you will trigger a bar to reentry when seeking to return.

Nothing in the law would prevent you from filing an EB-5 petition. Do speak with the lawyer who can review your asylum application to make sure there are no inadmissibility issues. And make sure to follow through with your asylum application as requested by USCIS.

It really depends. More information is needed to learn how you entered the U.S., and when you filed your asylum application.

Typically, multiple immigrant petitions can be filed at the same time, with whichever getting approved first and having a green card available (as per the Visa Bulletin) being used to move forward with Adjustment of Status.

Yes; you can apply for EB-5, but the issue will be your eligibility to adjust status or to the immigrant visa process if you cannot AOS. You should speak with an experienced immigration attorney who can advise you on the rules, i.e., eligibility for adjustment of status, any unlawful presence reentry bars, etc.

Yes, you can. If you applied for asylum before your status expired, you may be able to get your green card in the USA. There are some disputes about this.

Yes, you can, but if you have not been maintaining status, then your final stage processing may need to be done overseas. Asylum is not status; it is just a period of stay authorized by the Attorney General.

Yes, but you may not be eligible for adjustment of status unless you have maintained your nonimmigrant status.