Is there any microcontroller that can make more than one thing at once like analog read and digital write or serial communication?

Arduino is the microcontroller

There are many microcontrollers that are out there that have the capability of performing an analog read, a digital write and serial communications. The majority of modern microcontrollers ranging for the PIC18F4XX series and Arduino have the capability of using RTOS for operation in which several tasks will be perfomed simultaneously.

Now a days there are different micro controllers with builtin modules, a micro-controller with a hardware serial can simultaneously read/write serial port and utilize digital IO.

more over you can use real time RTOS with micrchip or atmel micro-controller for  real time operation.

Microcontrollers with multithreading that are running on same clock but run independently can do that. 

Most of microcontrollers can handle multiple tasks at a time, and that is done with the aid of interrupt services.