Hello, I am total noob at playink CK. There is few questions I want to ask
1. How I can earn gold, I am always losing it
The first thing I do is look to see if I have anyone who need to be married. If I have a male ready for marriage then I go to the report screen #5 which tells you available brides. Then I sort on ST which is for stewardship. Then, if the male being married is 16, I sort by age and try and get the highest ST on a 16 year old available female for marriage and propose that marriage to the owner of the fief she is in. Sometimes, at the beginning of a game, you need to wait a few years so that the characters can have their traits go up so you can find a good steward. This can drastically add extra income for you.
Then, fief-wise, the first thing I try to build is a forestry or whatever it is for 100 gold. I keep repeating this as money becomes available. I also keep repeating trying to find high stewardship ratings for potential brides.
2. How I can hire more army, and how I can provide my army when it's on field and how I can return in to castle?
This has already been answered somewhat.
3. How I can earn more prestige and piety?
You usually get a small amount per month of each without doing much. But, eventually, you'll need to probably get it up to +1.0 or better per turn. This can be done by acquiring titles. Also, creating titles can add much prestige to you. Creating a a title of king for yourself creates a lot of prestige. Sometimes gaining prestige is as easy as eliminating the negative effects on your prestige, like a son that is of age and landless.
4. How I can break from kingdom and make my own kingdom?
I'm not sure how to do it on your own, but there are events that ask you if you want to break away. These happen pretty often if you keep doing things that hurt your loyalty. Sometimes you get an event to lower loyalty by scheming against your liege. If you keep taking the ones that lower your loyalty, you'll eventually get an event that states, "It is time to break away from your liege." And you can choose to mend your relationship some or go ahead and choose to break away. I got an event that allowed me to break away without bloodshed (if your liege is not willing to fight you to get it back).