Ford Focus Titanium X Navigator 2014, MK3, Errors - ABS, Traction control and Hill Assist lights coming on?!

Hi guys, I'm new to the group so a quick introduction. My name is Matty and I drive a lovely Ford Focus Titanium X Navigator 2014, 49k milleage. I know my basic car stuff and that's about it, hence why I'm asking the below.

On my commute to work this morning (20 miles to Sheffield down the A1 then M18) my ABS and Traction control lights came on and I felt the car shake for literally a second while driving, the speedometer stopped working and was at 0mph while I'm sure I was going over 50mph! (The car drove perfectly fine) This happened when I left a rounadbout and joined the slip road. I made it to Sheffield but near the car park I was stuck at traffic lights, so I thought switching the car off and on might do the trick (like you do!), but the car didn't even want to turn off. I got to the car park and the car turned off after couple of tries (pressing the Start/Stop button). I called AA and a guy inspected the car by checking the alternator and disconnecting the battery, but nothing worked. He did the computer checks and errors C00344A and C003407 appeared on the screen, so he inspected the front right tyre and calliper, and found a strange scratch along the disc (looked like a stone was stuck between the disc/pad?), he then deleted the error messages and I managed to get home without the errors reappering on the dash.

Have you guys come across anything like that? The ABS sensor was also checked, taken out and put back in to see if it looks faulty, but everything seemed fine.