I'm no Diet master Bro. But 250 gms a day is pretty decent. You should aim for 1.5 to 2 grams per pound of Body weight. so 1 kg of weight x 2.5-4 grams of protein = daily intake.
5x5 worked wonders on my strength and size. But I was taking more supplements.
Working out 3-4 times a week is dependent on the individual. I worked out 4-5 times a week. But skipped some days if I the current work out muscle group was still sore. Sometimes I relpaced the weights with cardio. Then made sure I got to bed earlier and kept on my diet.
Being a slim guy sucks bro. There are so many sources for Losing weight and so few for Hard gainers.
Your in the right spot for info. Some of these guys have been in the game for 30 years.