You can mix synthetic and non-synth with no problems. basically you’re making a synth-blend, but for a cheaper price i’m sure. just don’t mix regular 2 stroke with marine 2 stroke or something like that. They have very different formulas.
Did you check your idle air control valve? mine was doing something similar because the valve went bad and the wiring was frayed. the valve has four wires running to it on your throttle body and are paired for what direction the valve moves in. they should both be getting system voltage