Intelligent reflecting surface (IRS) and movable antenna (MA) are promising technologies to enhance wireless communication by reconfiguring channels at the environment and transceiver sides. However, their performance is constrained by practical limitations. To address this, we propose a multi-functional antenna/surface system that leverages their complementary advantages. A rotatable IRS (R-IRS) is deployed to enhance downlink communications from a six-dimensional MA (6DMA)-equipped base station (BS) to multiple single-antenna users. To reduce the complexity of real-time channel estimation and beamforming, we formulate an optimization problem to maximize the average sum-rate using a two-timescale (TTS) transmission protocol. Specifically, the BS antenna configuration (including position and rotation) and IRS rotation and reflection are optimized based on statistical channel state information (S-CSI), while BS transmit beamforming is designed using instantaneous CSI (I-CSI) in the short timescale. We first consider a single-user case and show that the 6DMA at the BS should form a sparse array for multi-beam transmission towards both the IRS and the user, allowing efficient coordination of direct and reflected channels, while the IRS rotation achieves effective multi-path alignment. For the general multi-user case, the optimization problem is non-convex and challenging to solve. To tackle this, we propose an efficient algorithm combining weighted minimum mean-square error (WMMSE) and stochastic successive convex approximation (SSCA) techniques. A low-complexity algorithm is also proposed to reduce computational complexity. Numerical results validate the proposed system, showing significant performance gains by jointly exploiting the spatial degrees of freedom of the 6DMA-BS and R-IRS under the TTS protocol.