is sublimation a process that occurs under the temperature of the boiling point?

Answer 1

yes.it actually occurs under the melting point too

Answer 2

Sublimation- is the process where a solid fluid "evaporates" directly to a gas. An ice cube in your freezer will gradually get smaller & smaller as it sublimates away. Obviously this can happen at temps well below freezing. Personally, I've observed this happening over a period of weeks to icicles hanging off of roofs during the winter up north.