What is unintentional? Is there any reason not to study hard?
Holding a three-inch pen: In the past, you had to hold a pen (a three-inch long brush) with your right hand to read and write.
Dont Ask For Help in Winter: In the past, the poor were the most sad in winter. They were hungry and cold, with no clothes to wear and no food to eat. "Go to Dont Ask For Help in winter" here means that when you study hard, have cultural knowledge and the ability to make a living, you are not afraid of poverty, cold, hunger and need not ask for help.
Generally speaking, it is to encourage you to study hard and exercise your earning ability by serving the public.
The famous saying can be used for reference: if you don't work hard, the boss will be sad.