In The MPLS LSR if I have 4 INPUT ports with 4 labels
label:port 11 : 1 22 : 2 33 : 3 44 : 4
and ONE output port
How many labels can exit through the output port/interface? or do they get aggregated into one label?
It really depends on the implementation and the particular configuration/feature set on the LSR in question. In the event of some sort of path protection mechanism (i.e. fast reroute) an additional label may be applied (or popped) to accomplish a bypass. Normally, however, the LSR should normally simply be swapping the outermost label based on whatever LSP bindings have been previously signaled.
This sounds to me like a homework question - in which case the answer (beyond actually doing the assigned reading and research yourself) is that the label space in use on the outer label is normally only locally significant to the outbound interface and that, in practice, there is a separate binding for each LSP and hence a distinct outbound label associated with each inbound label.