Just simply, from the diagram above is p1=p3 and v1=v3?
If the viscosity is negligible, then yes.
If the cross sectional areas are the same and the flow is inviscid, then yes. From the diagram, it isn't certain that A1 = A3 though.
If the flow is inviscid, then the inner flow at section 3 can't be determined. With zero viscosity, there's no reason that the flow from section 2 couldn't simply continue with the same diameter as the tube in section 2, flowing at v2 while the surrounding fluid in section 3 isn't moving at all, since there's no interaction between shear boundaries with an inviscid flow. The "average" net flow v3 should be the same as v1 since mass flow is constant, assuming section 3 diameter is the same as section 1 diameter.
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