If I eat low-calorie food 6 days a week, and eat whatever I want once a week, would I still lose weight?

no you have to eat low calorie foods all 7 days or you will gain back all that you lost

I have been doing 1800 calories a day, 5 days a week, and 2 days a week I have a "free meal" (and then my other 2 meals light)....it's been working great for me.....and it's much more fun that never eating what you want.......

if you eat less calories than before and get the same amount of exercise, in general you will lose weight.

yes you will still lose as long as you do regular exercises. read more tips on weight loss, calorie burning and exercise programs to help you better on this site

not if u dont exercise. and why not eat whatever u want all the time? you just have to learn control and portions. that doesnt mean eat cake everyday.

my sister use to do this when she first started dieting, but as she saw the pounds come off she didnt want that free day anymore because she wanted to lose more weight

so yes it does work

and goodluck!