I think by now you must have managed to do the required steps on the netcd file. Just to highlight, you can also read the netcdf file directly as a raster brick in one single step, and then convert to data frame. The same operations (extraction of required spatial domain using the spatial points) can be done on the raster brick object. See e.g. below
Tried to follow the (your) code, i do not see the point where the .nc file is being used. Did you mean to create a dataframe from the .nc file? as.data.frame(), or use a combination of as.vector(nc.array) and matrix(dims of brick).
Sadiya Tijjani Baba : When you read the netcdf file as a raster 'brick' object, each layer would represent the time dimension in the brick object (This is assuming the netcdf file structure is lon, lat, time; where time could be days, months, years etc).
When the raster brick is converted to Dataframe, the first two columns will be Lon, Lat (in the above case, the lon, lat of the raster pixels over which the points fall). The columns 3 onwards would represent the value of the variable in months or years (whatever the time dimension of your netcdf). Assuming your netcdf is 20 years 1981:2000, you will have Lon, Lat, 1981, 1982...2000, wherein the values in each column represent your variable in that year, at the lon,lat location. Obviously, if your netcdf file is monthly (instead of annual), the columns will become Jan 1981...Dec1981, Jan1982...Dec1982...Jan2000..Dec2000. You can rename the columns using 'setnames', or 'colnames' or just 'names' functions. See R documentation.