Seems like you're overthinking...
Can i connect the l3 switch and the router with just 1 cable(can 1 cable carry both l3 and l2 traffic)?
Since L3 packets are transported using L2 frames: yes, that is normal usage. You'll need to route across the L3 switch between the router and the remote VLAN:
L2 switch------L3 switch------router
Of course, the router can't talk to VLAN1 directly, but that's not required for L3 connectivity. Make sure the router gets a routing table entry for VLAN1's subnet with the L3 switch as gateway. The L3 switch can probably use the router as default gateway.
If you do need VLAN1 over L2 you'll need to use a VLAN trunk between L3 switch and router, and add VLAN1 to that.
If i can what should be the protocol i should use ?
The most common protocol is IP (v4 or v6) over Ethernet.