Pretty straight-forward question. Read through Section One of the 802.3 standard, and I found a nice model of a MAC frame that gives me extra insight, but I see that this question is not asked anywhere and I can't find a straight to the point answer anywhere else.
Technically a packet is a layer 3 protocol data unit (PDU). But yes, PDUs are generally referred to as packets.
As previously mentioned the OSI model is a theoretical model. Though to answer your question, not all layers have headers.
Layers 5 - 7 are typically just referred to as data.
Layers 2 - 4 have headers.
Layer 4 - Transport - TCP header.
Layer 3 - Network - IP header.
Layer 2 - Data Link - MAC header & FCS footer.
Layer 1 does not have headers as it is converted to binary data.
The OSI model is a theoretical model, and the real world often deviates from it. For example, layers 5, 6, and 7 are generally combined because the OS programmers never implemented them. Layers 1 to 4 generally map to the OSI model, but even there, there is some controversy about it.