The first thing we do in the Sprint is to plan. Yes, we still have some forms of planning in Agile.
The Sprint Planning meeting is 8 hours in a one-month Sprint, and shorter proportionately for shorter Sprints.
Sprint is the Scrum term for iteration. Iterations are cycles during which we focus on a subset of features and create a usable product.
Sprints should be shorter than one month. We usually prefer shorter Sprints. Two-week or three-week Sprints are the most common choices.