How to digital read and send the data through serial to PC with speed around 2 MHz?
In short? You can't.

To have a 2MHz transmission you need 2*Nbit MHz of serial clock to send it to the PC, where Nbit is the number of bits per sample. Since the minimum is 8, englecting the synchronization or additional bits the serial clock has to be at least 16MHz. Which is the system clock of the nano. So no way.

Now, with the alternatives. First question: what is your ADC's interface? I found the LTC2204. It is a parallel ADC, so you need something to convert it to anything readable by the PC.

I'm not sure about the feasibility of this, but a nano is not enough. I'd use an STM32 (because I have their Nucleo boards, but you can search for other 32-bit boards) and a high speed serial interface. Since even SPI can be slow, maybe ethernet needs to be used. I was not able to search for boards with native ethernet interface; anyway the STM32F4 microcontrollers should (see this article) have an ethernet interface and you will "only" need the PHY. I think that this is the only applicable way to follow..