Can I invest in REITs with FSMOne? If not, what are some recommended brokerages or platforms to invest in REITs?

Since retail investors and finance professionals cannot robustly predict the fate or performance of single stocks or REITs, the better choice would be a REIT-ETF.

From the 3 Singapore domiciled S-REIT ETFs the one most focused on Singapore itself is:

Lion-Phillip S-REIT (SG:CLR)

Hi I think most platforms do offer REIT options like Ascendas REIT (SGX:A17U), CapitaMall Trust (SGX: C38U) or First REIT (SGX:AW9U). Personally I am using SCB.

As far as I know, you may even choose to do RSP to certain REIT options or REIT ETF via OCBC's BCIP plan.