Yes, all Spyders use the same barrel thread so any spyder threaded barrel will fit. The MR4 has that shroud on it that the barrel has to go into, so just stay away from those few barrels that are thicker at the base.
The APEX is a barrel made by BT. Its got an adjustable tip which puts backspin on the ball as it leaves the barrel which adds extra range to your shots. The barrel itself isn't so good but you can buy just the tip that puts the spin on the ball and put it onto APEX ready barrels, which lots of companies make now.
Rifled barrels are NOT more accurate than other barrels, thats a myth. Heres link to a video with a lot of good info on barrels!