Learn English – The meaning of “out of question” vs “out of the question”

The first sentence, "had my car cleaned," implies that someone else did it. "I had my car cleaned [by someone]." Disregarding tenses, you could say "my car was cleaned." The "had [something done]" setup typically implies that you instructed someone to do it.

The second sentence means that you cleaned it. Disregarding tenses again, you could say "I cleaned my car."

The writer is creating a phrasal verb:

to schedule something|someone out ....

meaning

"to eliminate the possibility of something (unscheduled) happening by chance, by scheduling an activity for every available time slot"

Here, the "something" is "the unexpected".

The author is saying "Leave some time unscheduled so that the unexpected may enter your life".

Compare "to rule out".

When we rule something out, we exclude it as a possibility.