Toyota Prius v 2013 showing message'' when parking, apply parking brake securely'',any help??,thanks

Hi there this is not a common fault unless the emergency brakes does no have enough free play, do remember this SUV has a dual function brake caliper hydraulic piston should be depressed in a specific manner and brake fluid system should be bleeded for air bubbles .On rare situations a bad quality disc pad could cause this kind of issue.

Assuming you Prius is an automatic gearbox, it sounds like there is a problem with the neutral safety switch, sometimes called a transmission position sensor.
This is a switch that won't let the vehicle start if it isn't in neutral or park. Yours sounds like it isn't reading the gear it is actually in. Using you parking brake, test to see if it will shift into neutral and try starting it. If it won't shift or won't start it is probably the sensor.
The sensor can be located next to the shifter inside the car OR on the gearbox itself. From the replacement quotes I've seen I think it is on the gearbox.

i have a 2010 Prius that we bought new. It has had no problems, but I can tell you from my study of the Prius that pretty much nothing is simple. The easiest way to reset stuff is to disconnect the a start battery connection. You can look on the net how to start a Prius with jumper cables to the engine compartment, and disconnect the start battery there. If you are not comfortable with that, the start battery is in the rear near the spare tire. Disconnect the negative cable only, wait 15 minutes and reconnect. You may have to reprogram your radio push buttons, but so what. If this doesn't work, take it to a shop (maybe toyota dealership) that can read and interpret the trouble codes for a 2010 Prius. Enjoy the car, we do.

I’m happy to assist further over the phone at https://www.6ya.com/expert/bill_f6ca18ca1db028ed

you can if you ride the brake --city driving with lots of traffic will wear down brakes --if brakes become damaged

the traction control and abs works as one, check the air pressure in your tires

The ABS system is in need of immediate service. The hard pedal is the ABS/Hydraulics malfunctioning and beeping to let you know. Could be a sensor or module maybe a wiring/connection issue but have it serviced ASAP . A bad vacuum supply to the booster or booster diaphragm can also cause a hard pedal and any could light the warning light.

VSC ABS and ! lights plus red (!) - Toyota Prius Forum ...

www.priusonline.com/...toyota-prius.../19804-vsc-abs-lights-plus-red.ht...

Jun 3, 2008 - 8 posts - ‎3 authors
If the accumulator fails, you will get a red brake warning light and the pump will now run continuosly until it burns out. ... hydraulic pressure to the brake system and "no"red warning lights. .... Fog Lights, PassGas, Toyota Prius General Discussion, 4, 10-13-2005 09:12 AM ... 11-13-2015 10:01 PM by Tim Lee.

Alarm with Brake Light, ABS, VSC and amber warning lights ' PriusChat

priuschat.com > ... > Gen 2 Prius Care, Maintenance and Troubleshooting

Jul 26, 2005 - Later that same day - I started getting an alarm - as soon... ... Gen 2 (2004-2009) Toyota Prius Forums > Gen 2 Prius Care, ... Discussion in 'Gen 2 Prius Care, Maintenance and Troubleshooting' started by NorthStar, Jul 26, 2005. ... I am getting the red BRAKE LIGHT, the amber waming symbol, ABS, and ... VSC, ABS, (!) and emergency brake light on
Feb 5, 2010
Brake, Brake warning, ABS, VSC appear
Oct 5, 2008
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there are several places to start with some thing like thisif this is a 2008 and the breaks failed take it back to the dealer. this could have been worse brakes are nothing to play with

no the P light ans system will always be on unless you command a drive or N funtion since there is no 'park' in the drive train only a mechanical brake. when running/on, when you put in drive it should acknoledge drive and P should unlock. if not you have trouble and need the dealer