Student or Learner
1. I'm the most over-scheduled man on the planet.
--- Does it mean he is disorganized or has too much things to do?
2. My parents suggested I might be up to this task in the first place.
--- Does it mean they thought I might be the most suitable person to do this task?
1. He is too organised; or rather, his time is too strictly allocated.
2. His parents thought he was capable of the task. The use of "up to" suggests that it was a task that might be considered difficult.
Cf. the use of "up to" for "engaged in", where the activity is dubious in some way, e.g.
3. I think he's up to something.
All the best,
Not a professional ESL teacher.