In answer to your questions and based on our experience, yes and yes. I usually put my feet on top of the bag I have beneath the seat in front of me.
My husband and I have 2 different doctors both of which have told us we should wear compression socks most of the time. After resisting, he's religious about it. Me...not so much. There are 3 levels of compression: light, medium and firm. FootSmart has an excellent selection of them: http://www.footsmart.com/compression-socks-s.aspx. You can also find a good selection at Amazon.
We both need them to cover the foot and go up over the calf as close to the knee as possible to aid in circulation and keep swelling down. I prefer the cute ones like those made by Sockwell. He likes the dorky white athletic-type ones. We both get medium/moderate compression.
Now here's a little story. Our son is a pilot. He injured an ankle while hiking. It was taking a long time to heal and interfering with his work. He had quite a bit of bruising. He showed us the bruising one day and my husband gave him a pair of TravelSox. He wore them the next day to work and later let us know that he was a convert. They improved his circulation so much in one day that all the bruising went away. They were medium compression. Our son has chicken calves compared to his father, but the same size socks worked for both of them.