The sec 9(4) of cgst,2017 has been suspended till mar 2019. So Rcm is not required to be paid.
And with regards to the Tax on rent..Your partner has to see whether his total turnover is exceeding the limit specified in the act. If yes,then he has to get registered and collect the tax on the rent from your firm and remit to the govt treasury...
Because in GST, firm and partner are different assessee. As Gst has got pan based registration.
Conclusion: the firm is not required to pay any tax for the time being.