New to the forum, New protege5 with a CEL and questions

ok just bought a P5 about a week ago, the check engine light came on and the codes are P0507 and P0421

sounds like the p0421 code is a bad cat on bannk 1?

also the P0507 code is somehting about the IAC and idle being to high anyone have any idea on what to check? is it the IAC thats bad or do i just need to adjust my idle?

i also noticed while looking under the car that there is a hose hanging in the rear of the car, by the gas tank and rear sway bar, IT IS NOT A GAS LINE nothing is leaking out of it and i cant even see were its coming from, i dont see anything what so ever in the area that it would connect to, anyone have any idea on this?

also the ABS and Brake light are one, ABS works just fine, fuse is not blown and it doesnt look like any of the ABS lines are broken at all, i checked the brake resivor brake fluid is above the normal line, and the float in the resivor seems just fine.

Weird thing is that they will both go off and on completly randomly they stay on more than they go off, im lost here and no the ebrake is not pulled at all and i checked the ebrake connection under the consol and it all seems fine

any help would be greatly appricated!

DTC P0507 - Idle Control System, RPM Greater Than Expected

DTC is set when actual engine speed is 200 RPM greater than programed target speed for more than 14.1 seconds with brake pedal depressed and front wheels in straight ahead position. This is a continuos monitor. MIL is illuminated when PCM
detects malfunction during two(2) consecutive drive cycles.
Possible causes are:

1. Accelerator cable misadjustment
2. Cruise control actuator cable misadjustment
3. Idle Air Control(IAC) valve malfunction
4. PCM malfunction
5. Throttle valve malfunction
6. Vaccuum hoses misrouted

DIAGNOSIS & REPAIR

1.Turn ignition off. Connect scan tool to DLC-2. Turn ignition on, engine off. Monitor for FREEZE FRAME DATA and ensure data has been recorded. Check service bulletins for repair information related to this DTC. If repair information is not available, go to next step. If repair information is available, perform diagnosis and repair as necessary. After repair, go to step 8.
2.Turn ignition switch off and then start engine. Using scan tool, check for DTCs. See RETRIEVING DIAGNOSTIC TROUBLE CODES under SELF-DIAGNOSTIC SYSTEM. If any other DTCs are present, go to appropriate test and repair first. If no other DTCs are present, go to next step.
3.Perform IAC valve inspection. See IDLE AIR CONTROL VALVE under IDLE CONTROL in SYSTEM & COMPONENT TESTING - MIATA, MILLENIA, MPV, PROTEGE, PROTEGE5 & 626 article. If IAC valve is okay, go to next step. If IAC valve is faulty, replace IAC valve. After repair, go to step 8.
4.Turn ignition switch off. Check accelerator cable free play. Ensure throttle valve is at closed position. Throttle cable free play should be .04-.11" (1-3 mm). If cable adjustment is okay, go to next step. If cable adjustment is needed, unlock White locking tab "A". Unlock stopper "B". If stopper "B" will not unlock, it may be necessary to carefully bend tab "C" out. To adjust free play, push or pull accelerator cable housing directly behind spring. See Fig 1. Turn stopper "B" to lock position. Ensure throttle cable free play is within specification. Move White locking tab "A" to lock position. Ensure correct accelerator operation. After accelerator cable adjustment is complete, go to step 8.
Fig 1: Adjusting Accelerator Cable
Courtesy of MAZDA MOTORS CORP.View Full-Screen5.Check cruise control actuator cable free play. If adjustment is okay, go to next step. If adjustment is necessary, push or pull actuator cable directly behind spring 2 times. Turn ratchet ring and slide lock lever as indicated. See Fig 2. After actuator cable adjustment is complete, go to step 8.
Fig 2: Adjusting Cruise Control Actuator Cable
Courtesy of MAZDA MOTORS CORP.View Full-Screen6.Check vacuum hose routing. If vacuum hoses are routed properly, go to next step. If vacuum hoses are not routed properly, repair as necessary. See VACUUM DIAGRAMS article. After repair, go to step 8.
7.Check throttle body. If throttle body is fully closed, go to next step. If throttle body is damaged or stuck, clean or replace throttle body. After repair, go to next step.
8.Reconnect all connectors. Start engine. Clear DTCs. See CLEARING DIAGNOSTIC TROUBLE CODES under SELF-DIAGNOSTIC SYSTEM. Depress brake pedal for 14.1 seconds or more. Check for DTCs. See RETRIEVING DIAGNOSTIC TROUBLE CODES under SELF-DIAGNOSTIC SYSTEM. If DTC P0507 is present, replace PCM and go to next step. If DTC P0507 is not present, go to next step.
9.Cycle ignition switch from off to on. Check for DTCs. See RETRIEVING DIAGNOSTIC TROUBLE CODES under SELF-DIAGNOSTIC SYSTEM. If no other DTCs are present, testing is complete. If any other DTC is present, go to applicable test and repair.

Please Note: "Fig #1 & #2" are not available; Please disregard; Sorry & thanks.

In regards to the ABS/Brake Light Issue:
As I understand it, when the ABS light is illuminated, the ABS system is NOT fuctioning and WILL NOT function as designed.
However, your Standard Braking system should work as designed.
Further more; When the RED brake light is illuminated, it is very possible that the standard braking system will NOT operate as designed!
I recomend that you have your vehicles braking ssytem diagnosed & repaired right away. I'm sure you don't need to be reminded of how dangerous it could be for you, your passengers & other vehicles on the road if your brakes aren't operating properly! Seriously , get that taken care of!
There,.... that was my public service anouncement for the week. ;-)