Yes, CAESAR can be used to model FRP pipe in a B31.3 analysis. That is the Code we (RPS) use most often. But you need to be careful with Expansion stresses. It is usually not recommended to include expansion stress cases as FRP is not a ductile material. Expansion-type stresses should be treated the same as primary stresses, so use Sustained, Operating, or Occasional as appropriate.
With regard to "Eff", I'm not sure what input you're referring to, but the "Elastic modulus/axial" is the axial modulus of the pipe; and "Ea/Eh*Vh/a" is the ratio of the axial modulus to hoop modulus multiplied by the Poisson ratio. It is common for FRP vendors to publish two Poisson ratios. Use the value that provides axial strain from hoop stress. For pipe wound at 55°, this will be the larger of the two values.