You will be unable to hem the draperies by machine as the stitch line will show and will look tacky. I suggest you face the hem by adding a strip of fabric and then hem by hand. Remember, use your walking foot. Make sure you have reduced your presser foot pressure, use longer stitches because velvet will "crawl". And, it cannot be pressed as is unless you have a needle board or you can press into a heavy towel. Could you consider using the cotton velveteen instead. It does handle a little easier. You could use binder clips on the inside to hold your panels together.
Regarding the pole question. Consider using PVC. It is strong and will have all the connectors and what you will need for corners, etc. Do not trim the selvages for the side hems. You are the only one who will see same. 1-1/2" side hem is ample. 3" double (faced) bottom hem is amble and heavy enough to hold it in place.
Gee, I hope some of this helps.