Agree with all the others, self-rising can't be substituted for AP in non-baking applications, and also with KayB that I don't keep it around any longer, since so few modern recipes call for it. Self-rising can be very easily substituted with AP flour, baking powder and salt. Ratio is for 1C self-rising, use 1C AP, 1/2 teaspoon baking powder and 1/2 teaspoon salt (salt in addition to what's called for in your base recipe).

Actually, it's been my experience you CAN use it if you're going to be flavoring the white sauce -- say with cheese, or a generous portion of spices or peppers. But I agree, a/p is much preferable. I don't even keep self-rising flour on hand any more.

No. Use plain all-purpose flour, or Wondra if you can find it. Self-rising flour contains baking powder and it'll give your sauce a funky flavor.

No, because self-rising flour is flour with salt and baking powder (the 'rising' part) already incorporated into it. Not the thing for a bechamel.