How to install this cheap metal curtain rod?
You're not showing all the pieces. What we see is a curtain rod and the center support.

There are brackets for the end that the rod hooks over.

Pictured is a dual curtain rod hanger bracket. The hole in the rod catches on the tang and it drops down onto the bracket.

The answer to your problem might be shown in the picture, use a nice board that spans across the window opening about six inches above. Use screws to hold it to the studs and then mount the curtain to that using stronger screws than came in the hardware pack. Graininess of the cellphone picture doesn't do the spar varnish finish on the hemlock board any justice.

For spanning that window (10') there are heavy-duty three piece curtain rods constructed exactly like these but with two of the screw-in supports available in addition to the end brackets.