Can a visa holder legally buy US stocks and real estate?

Yes to both. Buying and holding U.S. stocks, ETFs, or funds is open to any visa holder, it's passive investment, not employment, so it doesn't affect your status. Similarly, foreign nationals and visa holders can own U.S. real estate outright, whether to live in or rent out. What differs is taxation, not eligibility. As a nonresident alien, your dividends may face 30% withholding (or a treaty rate), while long-term capital gains on stock are often not taxed by the U.S. Rental income and gains on U.S. property, however, are taxable and may trigger special withholding when you sell (FIRPTA). The takeaway: you can invest freely, just learn the tax rules for your residency status before you build a big position.