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Answer to "Is this likely? I need a new logic board!"Unfortunatly yes, the logic board is going out, my macbook pro mid 2012 has a similar issue like yours where I will get random lines on the screen then it will attempt to reboot and give me the three beep error when it doesn’t.
Answer to "Why is black screen after replace it?"The reason you may not see anything on the new screen is because apple locked down the screen replacement, so if the computer sees a screen it does not recognize and is not programmed to the logic board it will disable the screen. There is no way that I know of to make it where the screen is programmed to the board, and I doubt apple will do it.
Answer to "HELP - New battery is not working!"If I remember correctly, Apple has it set up where they are the only ones that can reset the battery life information.
Answer to "Keyboard not working after water spill"So if I understand this correctly water got into the keyboard and now it doesn’t work. First thing I would do like somebody else mentioned is connect up a usb keyboard and see if it will respond to that, then make sure that the trackpad (how you move the mouse) is still functional if that is still functional then really all you need to do is replace the keyboard which depending on the model should not be that hard.