What do phagocytes secrete?
I think it would be hard to delineate what secretions are specifically because of phagocytosis, because in that sort of environment you have multiple types of cells secreting things, and multiple signals through such pathways as toll-like receptors (TLRs). So, I looked at papers involving activated professional phagocytes such as macrophages and neutrophils. The secretome of the activated cells follows a somewhat typical pattern for innate immune cells: IL-1ß, TNF family, interferons, IL-6, IL-8, and a host of other chemokines and cytokines (1, 2, 3). Mast cells of course secrete things such as histamine in response to Fc-receptor stimulation and TLR signaling. 

Non-professional phagocytes like epithelial cells lack receptors to make phagocytosis efficient, but I'm far less certain about the body of data on non-professional phagocytosis. We know that activated epithelium and endothelium secrete inflammatory signals to attract immune cells, for example, like IP-10 which attracts CXCR3-expressing cells.