1. How much protein do I need overall in order to gain mass/muscle in my butt?
A pretty good rule of thumb that's used in fitness circles is 1g of protein per lb of bodyweight each day, though various newer studies have shown 0.7g per lb to be just as effective. In your case, 80g of protein would be a good target, with 90g to 113g being ample.
As for overall calories, the discussion between JJosaur and mirower is quite informative. If you're only just starting resistance training, you may be able to get away with overall caloric maintenance (even deficit) and still build muscle as your body adapts to the new demands. Later on though, an overall caloric surplus will ensure that you continue to gain muscle mass.
There are a few good calculators out there on the internet where you can enter your bodyweight and level of activity to work out a basal metabolic rate, and then from there you can work out how much you need to eat to be in an overall surplus.
2. What types of food should I eat?
To gain weight in a healthy way, it's best to go for foods which are both nutritious and calorically dense. There are so many bodybuilding staples out there on the internet, but really you can't go wrong with eggs, nuts, seeds, fish, whole milk, butter, chicken, red meat, dark leafy greens, and as many vegetables as you can comfortably fit in. Fruit is generally good, being mindful of the sugar content.
3. If I make a protein shake, how much protein should it have?
Usually a single serving of whey powder will contain between 20g to 40g of protein. Again, there's some more recent evidence out there suggesting that 20g is a sufficient amount for a single shake.
4 What do I need to do/eat before a workout?
Since you're trying to build muscle, I'm going to suggest that you focus primarily on resistance and weight training. ExRx.net is an excellent resource showing you how to correctly perform movements with weights, minimising the risk of injury and getting the most out of the exercise. It's always a good idea to try the exercise with very light or no weight first to get the correct form, pacing and range of motion.
Since you mentioned wanting to work your butt, you'll likely be interested in movements like weighted squats and glute bridges.
5. Should I drink a protein shake before or after my workout?
While I agree with JJosaur that diet is really the critical component to be concerned with, there is a decent trend in the literature showing that 20g to 40g of protein consumed within a few hours before resistance training, and within 90 minutes after resistance training, is a good method of giving yourself the best chance of building muscle. Either can be as a meal or shake, and is largely down to preference.