Full-duplex (FD) radios at base station (BS) have gained significant interest because of their ability to simultaneously transmit and receive signals on the same frequency band. However, FD communication is hindered by self-interference (SI) and intra-cell interference caused by simultaneous uplink (UL) transmissions affecting downlink (DL) reception. These interferences significantly limit the ability to fully exploit FD's potential. Recently, movable antenna (MA) technology has emerged as a groundbreaking innovation, offering an effective way to mitigate interference by adjusting the position of each MA within the transmitter or receiver region. This dynamic repositioning allows MAs to move away from high-interference zones to areas with minimal interference, thereby enhancing multiplexing gain and improving spectral efficiency (SE). In light of this, in this paper, we investigate an FD communication system by integrating it with MAs to evaluate and investigate its effectiveness in handling SI and intra-cell interference. Moreover, we utilize rate-splitting multiple access (RSMA) as our multiple access technique in both UL and DL transmission. To achieve the full potential of the system, we evaluated three different scenarios with FD-BS-RSMA with MAs where our goal is to maximize the total sum rate of the system by jointly optimizing the transmitting and receiving beamforming vectors, UL user equipment (UE) transmission power, MA positions, and common stream split ratio of RSMA while satisfying the minimum data rate requirements of all UEs, common stream constraint, power budget requirements of BS and UL UEs, and inter-MA distance. The formulated optimization problem is highly non-convex in nature, and hence, we propose a gradient-based meta-learning (GML) approach which can handle the non-convexity in a discrete manner by optimizing each variable in a different neural network.