Do we need to project the netCDF file in the required coordinatte system for 25km resolution downscaled GCM Data(spatial reference :GCS_WGS_1984) before extracting the climate data using ArcGIS?
I am so sorry for late reply, I was really busy these days.
Anyway, regarding to your question, I should say no, you don't need to project them again, because they have been projected. so you need to read the metadata of your NetCDF files.
Attaching one of your files could help me to show how to extract the data.
It's depend on your model. What is your model? What is domain and scale of your model?
You can read data from netcdf file by using Netcdf Extractor in http://AgriMetSoft.com/Netcdf-Extractor.aspx
It's a windows software for extract time series from netcdf files.
But about calculate your grid number, it's depend on your model. If you have domain of your netcdf file you can use 'Grid Number Calculator' Api that there is in Netcdf-Extractor V1.1 or higher.
Besides that, you can watch many video about calculation of grid number(origin and shape) in my Chanel in YouTube