what is the role of IGP in MPLS network to route the customer traffic or to make the reachability
What is the role of IGP in MPLS network
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First, I would recommend checking out Cisco's MPLS FAQ For Beginners, or the NANOG Presentation "MPLS for Dummies" by Richard A Steenbergen. They both have some really good information.
With that said, let me address your questions one at a time. (I have excerpted them in part below.)
1: After the initial convergence of the network, LSPs now exist between all FECs which are typically interfaces on LERs that connect to a subnet.
Yes, LSP's exist towards all reachable FECs. And an MPLS packet could now be switched across the network.
2: Assuming that baseline is correct; How does R1 know it is an LER for an LSP that spans to R6 for example
R1 has no clue that it is part of an LSP that spans to R6. It only cares about the local/connected labels and FECs. That is part of what makes MPLS Label Switching fast and effective. It doesn't have to know the whole path. The router just knows that to reach FEC1, I apply label 1234, and exit interface XYZ.
Then later hops in the path utilize the same process, swapping in the appropriate next hop label and switching the packet on.
As for the bottom line question How are the LERs determined?, a router itself doesn't really know or care if it's an LER. It just knows that when it receives a packet destined for a local destination, with no tag, it delivers it.
In your output above, you can see that the first 4 outgoing FECs have Pop tag listed as the Outgoing Tag. A packet leaving R1 for one of the local subnets on R2 or R3 simply has it's tag popped and forwarded out the appropriate interface.
When R2 or R3 receive that packet, they see no label and process it via the normal routing process which delivers it to a local interface.
To quote the Wikipedia article on MPLS:
At the egress router, when the last label has been popped, only the payload remains. This can be an IP packet, or any of a number of other kinds of payload packet. The egress router must therefore have routing information for the packet's payload, since it must forward it without the help of label lookup tables. An MPLS transit router has no such requirement.
This is quite complex to answer in simple set of questions, but let's try:
Yes, it's possible to have internet connectivity by means of MPLS cloud, but it either means you need to self-deploy MPLS L3 VPN for yourself, or your MPLS cloud will be provided by upstream ISPs.
Usually, edge routers - the ones running MPLS, are distinct from L3 switches/routers in aggregation layer, specifically, that You also add firewalls to the picture. It's doable, but usually it's better to route at the switching layer not aggregation/edge layer.
You're trying to ask very specific configuration question, not specifically technology one. It's possible to separate VLANs by means of various techniques - splitting the access ports to access and trunk is very weak and unsecure method. Please take a look at Private VLANs as one way, the other would be the firewalling segment to take responsibilities of filtering traffic between hosts or networks.
Again, hard question. In this specific topology yes, they can be placed this way. Depending on the performance required or features required, they may however be required to be positioned in a different way.
"Common servers" availability will be governed by configuration, not topology. We have too little data right now to decide if that's feasible or not. MPLS can be used to transport traffic of different protocols, including IPv4 and IPv6.
Yes, it's possible to use IPsec over MPLS. IPsec is IP based, MPLS is transport technology for IP - be it IPv4 or IPv6.
Best Answer
IGP in an MPLS network advertises the internal topology. It provides connectivity for MP-BGP inside the network. The routing table in every router is also used by LDP to generate labels for every route.
The IGP caries no customer routes. That is handled by MP-BGP.