What is considered an average weight for a 24 year old female who is 5 foot 4 inches?

150 or less. Weighing 150 pounds or less would give you a normal bmi, less than 25.
It varies... It depends on your "frame" size, but height and weight charts are all over the internet. These give recommendations, but differ for each person based in age and level of activity as well. http://www.healthchecksystems.com/heightweightchart.htm.