+1 for major service. A focus will keep on going and going, but they need to be maintained to a high standard. I have a customer with an '03' 1.8 zetec over 400k on the clock, and she's as sweet as a nut. Don't skimp it will only cause problems in the long run.
Speed Pulse Sensor failure. It's such a common fault So common i'm just about to change mine for the 3rd time as I'm having these issues too. Might be an idea to dump and refill the gearbox oil as the failure 9 out of 10 times is due to swarf contamination.
Your missing a live, that's why the unit is shutting down after the correct code is entered. it's either poor fitment on the bluetooth kit providing once kit is removed it's fixed, or possible fault with headunit/wiring
Ford locks always pulse on the CL system, its the way they are designed but it's not supposed to be every 20 seconds every 5 minutes if memory serves. The radio removal should not in any way affect your central locking, I have fitted THOUSANDS of radios and several hundred to focus's I have never heard of or seen this fault. I'd probably get it into the stealership and have a diagnostic performed.