If I wanted to say "I ate something this morning" or "Did you eat something this morning", would I use a particle with "this morning"?
You have a choice; You can say it with or without 「は」. The more informal the speech, the more often the 「は」 is dropped.
The only situation in which 「は」 is not optional and it must be used is when you talk about what someone ate/will eat this morning in comparison to what he ate/will eat on another day. That is always 「けさは」 as 「けさ」in those cases is an importat topic.
(The common mistake among Japanese-learners that I have been witnessing is to use 「に」 instead of 「は」 with words such as 「けさ」,「きょう」,「あした」, etc. .)