Can I keep investing in Indian real estate as an NRI, and how is rental income handled?

Yes. NRIs are permitted under FEMA to buy residential and commercial property in India (but not agricultural land, farmhouses, or plantations). Rental income is India-source, so it's taxable in India, typically with TDS deducted by the tenant, and you file an Indian return to settle the final liability. The rent must be credited to your NRO account. On the US side, because the IRS taxes worldwide income, you also report the net rental income on Schedule E of your US return, where you can deduct expenses and depreciation. You then claim a foreign tax credit for Indian tax paid to avoid double taxation. Keep both countries' figures reconciled, and remember the property doesn't need FBAR reporting but the NRO account receiving the rent does.