Is it possible to redistribute routes that are fetched from MME/Mesh to BGP/OSPF/RIP and the opposite ?

If yes, how can I achieve it ?

no, cause there is no routing in MME/MESH. Its all Layer2 stuffs. Hence, no Layer3 routes. Now can you send layer3 routes over a MME/MESH network, yep!

MME is not L2. For example Quagga and Batman may communicate, why not MME and Routing?

MME is based on batman which is layer3. batman-adv is layer2.