Should it be “seeing him off”?

"Seeing" him off would suggest she went to the station to see him off and say goodbye, like you would when someone's going on a cruise or train trip.

"Sending" him off would imply she's actually sending him somewhere, like to camp, or jail, or a trip.

Just to be confusing, you can also send someone off with a flea in their ear Look that one up

I get the feeling at the OP is planning some sort of coffee table book called Grammar arseholes, or something similar, where she points out minor grammatical mistakes in Singaporean publications over the last 50 years.

And a goodbye party for someone is also called a 'send-off', whether it's for a short or long time (or forever, in fact).