ermm whether you need the protein shake everyday depends on your diet actually.You should be getting at least 1 gram of protein/ pound of body weight per day,since your weight=53kg=116 pounds,you should have at least 116 grams of protein per day.However that is the minimun and is for maintainence of present amount of muscle so to build on more muscle,you will need more protein than that,ideally 1.3-1.5 g/ pound of body weight so 150-175 grams of protein per day.So you should be checking on the amount of protein you take from your meals and if it is not enough then your protein supplement will then come in to top up.
Also to build up mass,you must have excess calories intake over your present weight maintainance calories intake=weight in pounds x 15= 1740 calories per day for you.If you do not eat in excess,there is no way you will grow.
As for protein shake,you should preferably take it after your work out cos that is the time the body desperately need protein to repair the worn out muscle from your work out,but ensure that you have carb either in the shake or soon after the workout in the form of a proper meal within 1 hour of workoutTo add carb to your shake,you may consider buying glucolin (can get from NTUC easily) and add it into your shake,around 40-50 grams of glcolin.Glucolin is actually glucose then when broken down by the body will become carbo and thus be used as the preferred choice to replace body glycogen level (preferred body fuel) depleted from your work out.If you just take your protein shake without a source of carbo,the protein will just be converted to become glycogen and used to replace body energy level instead of it being used to repair and grow muscle.
Also your work out is too simple to get any results,to gain mass,you must be doing compound exercises with the big 3= Squats,deadlift and Benchpress.These are excercise that involve more muscle set and thus give more growth per period of training as compared to just doing isolated exercise like your bicep curl which just work out that tiny bicep muscle.You reps are also way too much to do much for you.Generally if you can do more than 15 reps per set of exercise,that weight is way too light for you.Aim for reps of less than 6 if you are aiming to gain strength or 7-12 for body mass gain.Do around 3 sets for each exercise.And btw the only exercise you are doing now that will give you any noticable gains at all is your chin ups only,chins up is also a form of compound exercise as it involves a few muscle groups like tricep/bicep,back,lats,deltoid (shoulder),so you should continue to include that into your workout plan.In summary,you should aim to concentrate mostly on compound exercises and add in isolated exercise sparsely (maybe around 30-40% of your total training workout)
Lastly i notice you are training at home with your limited weights,but what you have is really too little for a proper workout so unless you start going to a gym,you will be wasting most of your protein usage potential.
Here is a pretty good website for you to find out some exercises you can start picking for a workout,come with gif pictures so it shows you how the exercise is actually done.Good luck,there is much more with regards to good workout,but what i have stated are just the basic,if you want better knowledge in this area,you will have to do your own research on the internet.
http://www.shapefit.com/training.html
As I have a station gym at home and a pull up bar it limits me to do different types of workout for example bench press etc.. But i will definitely try the workouts that u recommended me and also read up the websites. Anyway can i drink protein shakes during the days when i dont work out?