Trip from Osaka to Narita Airport

Hello,

We organize a trip to Japan and our returning flight is on April 13th at 17:10 from Narita Airport.

We are wondering if it is OK to travel directly from Osaka on April 13th, in order to arrive at the Narita airport around midday (say around 12:00-13:00).

Questions:
1- Is there a direct fast train between Osaka main station and Narita Airport? (we will be travelling with the JRPass)
2. In any case, how long is the trip normally by the fast train and are delays common in this route?
3. In general: would you recommend the direct trip the same day? Or would it be better to arrange staying the night before in Tokyo?

Thanks a lot for your help!

BR, G.