Is 'full employment' synonymous with 'the natural rate of unemployment'?
Full employment is a more general term, which has much less implication than natural rate of employment. My experience reading a lot of economics papers is that careful authors do not mix the two concepts.

Stricto sensu, full employment should mean 100% of the workforce is employed. But when we are talking about periods such as the trente glorieuses, the term is often used to mean "very low unemployment", which Keynesian economists associate with natural rate of employment. Politicians will most certainly never use the later, while economists may not always be very careful about which one they use.