Does Unity practice baptism and communion?

Yes, symbolically. Whereas baptism by water represents the cleansing of the consciousness, spiritual baptism signifies the inflow of the Holy Spirit. Baptism is a mental and spiritual process that takes place within the individual as he or she aligns with the spirit of God.
Spiritual communion takes place through prayer and meditation in the silence. The bread or the body of Jesus Christ symbolizes the word of Truth. The wine or blood of Jesus Christ symbolizes the conscious realization of God-life. Unity practices communion by appropriating or partaking of the spiritual energy represented by these elements.