RE: What is the order of execution done internally in ...
There is only one Primary input link to the Transformer and there can be many reference input links and there can be many output links. U can output to multiple output links by defining constraints on the output links. U can edit the order of the input and output links from the Link ordering tab in the transformer stage properties dialog.
RE: What is the order of execution done internally in the transformer with the stage editor having input links on the lft hand side and output links?
Within the transformer we have a toolbar which has following options: stage properties show all or selected relations constraints cut copy paste load column definition save column definition find/replace column auto-match show/hide stage variables input link execution order output link execution order. So we can set the order of execution of input and output links using the toolbar.