Does it have velcro in the loop so it doesn't slip off

Velcro isn't necessary be cause there's enough pressure on your foot (from your hand) that it won't slip. It's a wonderful device, especially following surgery if you have trouble raising your leg to get in and out of bed.

Is the loop large enough to lift a leg cast onto a bed

Yes it looks like it would be big enough. I only put it on my foot as I lifted my my leg on to bed after knee replacement. Was a great help.

What size should I buy for a 5ft. woman?

around 2 feet more or less should do it. one doesn't have to use the hand loop to swing the foot and leg around where you want the leg to go. I will say that it would have saved a lot of grief if the recipient of this tool had one of these long ago. as it is, she thinks it's pretty great. She can get into a car now without feeling like a turtle fighting to flip over from being on its back. She can lift her leg with a minimum of stress on her shoulders, knees and other leg.

What is the diameter of the loop?

I gave mine away. I have 10 1/2 shoes and they fit in the loop easily. I kept one in my car to help me get in and out and it was indispensable early in the healing process. I used it getting in and out of bed myself as well. I hope this helps.