How can we renew an Indian passport while the I-485 is pending?

If your mom has a pending I-485, she is in an authorized period of stay by the attorney general regardless of whether I-94 is expired after her entry on a valid tourist visa. She should be able to renew her Indian passport. She should not travel outside the US until she receives her advance parole card.

There is no problem with renewing your passport while an adjustment of status application (I-485) is pending. Whether she can renew it here in the US, or whether she will have to leave, is up to the Indian embassy. Remember she cannot travel with her B1/B2 visa while her I-485 is pending, however, and will have to wait to get her combo card (EAD and travel document, forms I-765 and I-131) to travel.

Seek renewal at the Indian Embassy. Should be no impediment that EB-5 and adjustment of status are pending.

Yes, she should renew her Indian passport by whatever way India indicates to do this. Some countries allow online and others require a trip back which she shouldn’t do until she gets her travel permit.

Yes, you may contact the Indian embassy in Washington and follow the process.