Do REIT ETFs behave differently from a Stock ETF during a market downturn? Are they riskier / do not have the same long-term advantages as stock ETFs due to e.g. rights issue to raise funds, dilution of shares, inability to repay loans?

The REIT etf is a basket of REITs, so if the market downturn affects every REIT in the etf, the etf will react accordingly.

Having a basket of REITs also protects you from having to subscribe to individual rights issue or a collapse of a single REIT. You get some form of diversification.

The etf will rebalance accordingly if there is a rights issue to maintain the portfolio allocation for each reit.