The only time you need to have it on bias is if it is going to be curved; then its important. I agree with others, on grain is the strongest. You want the part of the quilt that will be handled alot to be as strong as possible.

You can cut your binding fabric lengthwise grain, it just won't have the "give" that the crosswise or bias binding has.

Well, its on, and it sewed on fine, I havent hand stitched the back yet though, and its then i will know whether I like it or not. I think maybe it feels too tight, but we will see I dont have enough fabric to redo now so lengthwize it is!

Yes you absolutely can use length grain. It doesn't have as much stretch give but sure doesn't have seams. So use it just understand less stretch. You might have to go a bit slower and pin more due to nature of the give in the fabric.

I'm currently sewing on binding that is cut of lengthwise grain scraps. It's going on OK...