Yes both applications can run at the same time.
You should have no issues running Prosphere and ControlCenter concurrently.
ProSphere and ECC can be run together without issues as such. We just need to ensure SMI-S, SMAS (SMC and SPA) and ECC Symm agent dont sit on the same host as they all to use the same SymAPI.
It is ok to install ECC Symm agent and SMI-S together provided the SMI-S is the 32 bit version as it also installs Solutions Enabler and ECC Symm can talk to 32 bit one only.