Linear Actuator using Relays, MOSFET, and PWM
First and foremost, is the circuit safe?
  


In principle it's safe for ordinary applications but those applications that are "medical" or "flight critical" or require special approval it takes more than a few words and a hand drawn circuit to establish it's safe. The relay device is this: -



And the relays are rated at 30 volts and 10 amps so, providing the current taken by the motor is below 7 amps (a de-rating imposed by me) then I'd say it was safe if built correctly. However, I have no idea if Sunfounder" are a reputable supplier/manufacturer. They are based in ShenZhen in China so, ultimately you have to decide whether they are reputable because "being safe" implies so much more these days than making sure it doesn't catch fire or electrocutes someone.

If you require it to be somewhat "fail safe" then you have to consider the problem of disconnecting the MCU - doing so will naturally activate the MOSFET and run the motor at full speed. See also my final paragraph.


  
  What is the function of that 29VDC with a snubber diode that pulls the Normally Open signal of the relays up?
  


The snubber diode and resistor ensure that inductive kick-backs from the motor are routed back to the positive rail. This prevents the situation of having an uncontrolled back emf destroying the MOSFET.


  
  What is the function of the BJT?
  


MOSFETs usually require a decent gate drive voltage to ensure that the MOSFET acts like a switch (ohmic region of operation) and many will work happily with 5 volt gate drive voltages so, if you were connecting the circuit to an MCU that only produces (say) a 3.3 volt logic level, the BJT buffers the signal to 5 volt to ensure better MOSFET operation.

However, if your application requires that the circuit is "off" when the connection to the MCU is removed, you need to reconsider how this circuit operates. Currently, if the MCU connection is removed, the MOSFET will be switched on and the actuator's motor will turn and might cause a problem.