eth0 is wired to one port on the switch, and all LAN ports are wired to the switch, too.
eth1 is wired directly to the WAN port, there is no switch involved here.
The default configuration should not need to use VLANs at all (you should post it here, so we can have a look at it and confirm my theory). You just need to create the VLANs now, tag them on the CPU side, and mark them as untagged or off on each LAN port.
If the CPU port connected to the switch is eth0, use eth0.1 to go into the switch as VLAN 1 and eth0.2 for VLAN 2 etc. Once you are tagging VLANs on a CPU port, do not use the plain CPU port (eth0) for anything, always specify the VLAN number.
Some routers have a separate CPU port (e.g. eth1) connected directly to the WAN Ethernet jack on the back. Read the wiki page for your model to see how the hardware is arranged.
I guess my question is more about the difference between VLAN-enabled
switch hardware and software VLAN?
From what I gather from this discussion there is only one way to
configure VLAN interface.
Specific VLAN Id and custom interface name (xxxx.zzzz), regardeless of
weder it is VLAN-enabled switch hardware or software VLAN?
There are two parts. The hardware VLAN switching in the switch is set up with config switch_vlan statements. The switch is a separate chip than the ethernet port of the CPU. Sometimes they are built as different sections of the same chip, but still it acts like entirely separate hardware.
Software VLANs, eg. eth0.2, are used to send VLAN tagged packets out of a CPU port. The CPU port is connected to the switch chip by very short wires, but it is still logically completely separate hardware.
When setting up your Ethernet ports and switches, it is good to be logged into the router on wifi. This way you will not be blocked out if you misconfigure the Ethernet.
I have now two VLAN interface (eth0.1 and eth0.2) properly setup for
my device?
The line : 'option type bridge' is only needed when an interface is to
be bridge with an other interface (EG: wireless) or is it needed because
it is a VLAN interface?
I don't plan to use IPv6 for the moment that is why I removed the line
'option ipv6assign ...' from the try_1 interface. Same goes for the line
'option ula_prefix' in the 'globals' section.
I'm still missing something but I can't figure out what I'm missing.
As far as I know, yes: you have separated one LAN port from the others, and configured two independent interfaces.
You could bridge two ethernet interfaces (for example, to make them work as if they where on the same switch); but in your current configuration, it is configured as a bridge so the wireless interface can attach to it. It is unrelated to any VLAN.