Answer to Question 1
Answer: Weather deals with the short-term phenomena and state of the atmosphere. Climate is concerned with long-term phenomena and characteristics.
Answer to Question 2
Answer: Climatology and meteorology are concerned with the same elements of the atmosphere, but the time scale involved is different. Meteorology focuses on the short-term and climatology relies on the averages and variations of atmospheric conditions over years. As an example, climatology would document the distribution of tornadoes in space and time over many years for a certain geographical region. On the other hand, meteorology would investigate the conditions present in the atmosphere a few hours prior to tornado occurrence.