Non-orthogonal multiple access (NOMA) is a promising technique for ultra-reliable low-latency communication as it provides higher spectral efficiency and lower latency. In this work, we propose novel many-to-many (M2M) NOMA-based schemes to exchange broadcast, multicast, and unicast messages between cluster heads (CHs) of vehicular platoons. Specifically, we design uplink-M2M-NOMA (UM-NOMA), downlink-M2M-NOMA (DM-NOMA) and joint uplink-downlink-M2M-NOMA (UDM-NOMA) schemes for peer-to-peer vehicular ad hoc networks (VANETs). We propose a unique clustering design for full-duplex communication that utilizes the high throughput millimeter-wave (mmWave) channels. Furthermore, we investigate jointly optimal CH selection (CHS) and power allocation (PA) to maximize the network sum rate and devise a computationally efficient tailored-greedy algorithm that yields near-optimal performance. We also propose a super-cluster formation protocol to further limit the overhead of successive interference cancellation (SIC). The results reveal that in most of the considered scenarios, the proposed UDM-NOMA scheme outperforms orthogonal multiple access (OMA) in terms of sum rate by up to 50% even when the SIC receiver errors reach 10%.