Can I connect the ST Nucleo-F334R8 board using CAN (Controller Area Network)?
Can I use the CAN interface of the microcontroller or not?


It depends on yourself.


  I would like to connect the Nucleo-F334R8 to a different board using
  CAN (in the first instance and LIN afterwards). Can I do that by using
  just a couple of CAN transceivers (MCP2551)?


I don't know what's another board but for your Nucleo-F334R8 you only need a CAN transceivers (MCP2551).

Bear in mind that there are some software and Libs for using the peripherals of STM32. like:

CMX-CANopen
CANopen Industrial Automation for STM32, from CMX Systems Inc 

and

STM32CubeF3

and

STM32CubeMX

you can see all of them here(see All tab). use them for your job. that will help you to do your job quickly. I myself use them for operating the CAN interface.

Good luck!