Buying REIT shares for your own account requires no license of any kind. It's a brokerage transaction like buying any listed stock.
Where licensing enters is recommending securities to other people or getting paid for advice about them. Those activities fall under securities licensing and registration rules, which are separate from real estate licensing and vary in how they apply, so if you ever think about advising clients on investments alongside brokerage work, get that checked by someone qualified in securities regulation in your state before you do it. A real estate license does not cover it.
On insurance, the answer is no, and the reason is worth holding onto. When you own a rental you carry landlord coverage because you're liable for the building and what happens in it. A REIT shareholder owns shares in a company. The company carries property and liability insurance on its buildings as an operating expense, which is already reflected in the numbers it reports. Your exposure is the share price and the dividend, and neither is insurable.
What replaces insurance in this strategy is diversification and account structure. Brokerage accounts at US firms carry SIPC coverage, which protects against the brokerage failing rather than against your shares falling in value. Nothing protects you from a REIT's sector going badly, and sectors here diverge hard. Office and data centers have almost nothing in common as businesses. Owning a spread across sectors is the closest thing to protection you get.
