Do diuretics take away your appetite and make you feel unsteady when you walk or stand up?

They can do that. Among it smany side effects, dehydration is one of them. If dehydation is significant, you won't have an appetite, lower your blood pressure to cause orthostatic hypothension (low BP when erect) which can cause you to feel unsteady/fall etc.. Also, diuretic can waste away your salt and potassium which can cause arrythmias causing your symptoms. So, consult doc soon if you can. Good luck.