But doesn't the police have anti detector systems ( hope you understand what i mean) .
No. Detectors are legal most places. Check your local laws.
How about cop cars that have Laser's...Will the system warn me enough time in advance for me not to be clocked by whatever the cops are using?
No. If you are hit with laser, the V1 will tell you that you got hit with laser. If you were speeding plan on pulling over.*
Does it work only on the highway or in the city as well?
Everywhere. They excel on highways in my opinion for long trips.
Is the V1 or any other system undetectible?
Don't understand what you mean here. A detector is a detector. It does not transmit anything, it's like you listening to sound. So can someone detect that your ear is working?
And is there a way to install a v1 or anything else without it showing anywhere in the car? Say in the glovebox or armrest.
Nope, it's gotta be on the windshield looking forward. It's like eyesight. You can't see anything while hiding in a closet. There are (for $$) clean installs of other systems where you can't see anything. The hardware is in the grills, etc..
And is it detachable?
Yes, unclip phone wire, push button on top, it's off in 2 seconds..
And lastly how much does a V1 cost?
$400
And is the installation process long and costly?
Free, follow the hardwire DIY.. I can send you a link if you need
I thank you all for taking the time to read this and hopefully enlighten me.
Thank you
Feel free to ask more questions if you have them.. 
Go to their website by the way. Tons of good information there..
http://valentine1.com/
Good luck