>As a Roman Catholic convert to Orthodoxy do I need to be re-baptized? Should I anyway even if my priest says I don't?
Listen to your priest.
>Also is receiving Holy Communion before I've been re-baptized a sin?
You can't receive communion if you have not been Chrismated. Regardless of whether your Catholic baptism is recognized by economy, or it is required that you be baptized in the Orthodox Church, or you get a conditional Baptism, you cannot receive communion until you are Chrismated (Confirmed).
From what I know: if you were baptized by triple immersion, there is no reason your Baptism wouldn't be recognized. If you were baptized by aspersion or sprinkling, you weren't baptized correctly, but at the same time those forms are accepted if there is an urgency that prevents triple immersion. Normally your baptism will simply be recognized by economy, but the bishop/priest may instead request that you be baptized, or, if there is uncertainty as to whether you were baptized with proper form and intent and with faith, you might get a conditional Baptism.
In all cases, a question to ask your priest.
>Even if it was just a mistake? How serious is this?
People don't go to Hell over technicalities. Tell your priest you messed up once, and don't do it again. There is certainly a difference between "not discerning the Body and Blood of Christ" and "receiving communion too early out of zeal for the divine things".