You can change the prices day by day if you go to your calendar and click on the days you wish to change. Then press 'save changes' and you can set them as you wish.
For booking you will receive an email asking you to approve or decline the booking. If you click on the guests picture on their booking request, you can see their profile and any feedback on them. At this point, you can approve or decline them. You can decide on the level of customers you wish to accept (airbnb approved, friends only of airbnb etc) Its entirely up to you, but airbnb will always contact you by email if you have a booking enquiry. They have always to have verifications before joining the airbnb website, so you are protected. But it is you who have the final choice.