Hello Koushik
If the ISP is providing you with public ASNs, then it’s not a good idea to have the same ASN in all locations, because public ASNs should be geographically specific. There may be inefficient routing issues if you do that. However, if you’re using private ASNs then you can have the same ASN at each location if you choose to. Whether you do it or not depends on what you want to achieve. In this lesson, you can see an example of an MPLS topology where the two remote sites use the same ASN. In this case, you must use the Allow-AS-In feature of BGP. In this lesson, you have a similar topology but with different ASNs at each location.
I assume your question has to do with the internal network of the Intel organization, correct? You will typically have an IGP configured at each location, however, your routes will be shared with eBGP. In addition, the MPLS network uses an IGP as well, it can use OSPF however, IS-IS is the more common IGP used by ISPs. It may also be configured with BGP as well, although that is less common. So to answer your question, it depends on what IGP is configured and where that IGP is configured, but yes an IGP will typically be configured for this purpose.
I assume again that you are talking about the routing within the Intel organization (and not that on the MPLS network). If that is the case, and you want to use OSPF, the best practice is typically to create a different OSPF instance at each remote location and not multiple OSPF areas of the same OSPF instance. The OSPF instance in Ireland will redistribute its routes into eBGP, and so will each OSPF instance at each location. So there is no direct exchange of OSPF LSAs between locations. You can see an example of such a topology in this lesson.
iBGP is used within an AS. It is by definition BGP peerings that take place between BGP routers with the same AS, regardless of whether it is a transit AS or not.
Much of what you are asking is covered in the MPLS course which includes topologies similar to the one you describe in your post. I suggestion going over these lessons to more fully understand the details of such topologies.
I hope this has been helpful!
Laz