I cannot have 2 default route for 2 different vlans since it's considered as 1 switch now and has only 1 routing table
That's correct. Your two switches will have a single control plane. One switch will be the RE, and the other will be the backup RE.
Will both VR will be able to ping each other since they are on the same subnet ?
Yes, as long as they're also in the same VLAN.
Will they try to communicate using the vcp link or will they use the other link ? I would like to use the other link, not the vcp one, to pass the traffic between them
You need to think of the two EX switch in a VC as one single switch, not two. It's like you have a chassis switch, and each physical EX2200 is a line card (FPC).
Can I have 2 virtual router on the same subnet ?
Sure, as long as you follow the best practice of having one subnet per VLAN, and one VLAN per subnet.
Can I use the default routing table (inet.0) and the virtual router at the same time ?
I'm not really sure what you mean here
In general, I wouldn't recommend using a virtual chassis across sites. As you've seen here, it complicates matters, and while you can get it to work, it will be harder to troubleshoot later. Especially of someone else needs to troubleshoot it while you're on leave (you don't want work calls while you're on holidays/vacation do you?)