In case you can't setup a full-mesh iBGP and passing tables to SVC routers, I would suggest to setup an IGP between Core and SVC Routers and let it load-balance the default route.
Also you can have iBGP to SVC routers and publish the default route. So, if you get multipath enabled and the metrics to both Core Routers match, then you will also have two default routes on SVC routers. Keep in mind that you need to have it full-mesh.
Regarding HA in core layer, definitely iBGP between Core Routers would be the best strategy.
One point I forgot to add is, in case you are using Cisco routers, you might also need BGP relaxed best-path selection, which allows load-sharing between two similar routes from different ASs. You can read more here.
There are multiple ways to do this.
The other ASes could be sending a default route, or the router in AS100 could just have a default route configured.
The other ASes could just advertise their own routes through BGP.
The other ASes could advertise full BGP routes to AS100.
BGP has many factors which could play into the decision of which way to switch traffic destined to another AS. This is the subject of entire books, and it is beyond the scope of this site. It is far more complicated than IGP routing protocols, and it may involve many steps to determine the best path. Often is just boils down to how many AS hops away it is to get to the other AS.
You may be confused about the role of iBGP. The distinction of iBGP and eBGP is whether or not the neighbor is in the same AS. An AS will almost always have more routers than just the routers connecting to other ASes. The routers internal to the AS would have the same AS number as their neighbors, so they would use iBGP.
It would also be a huge discussion about how design within an AS. Again, you could have default routes, full or partial routing tables, a combination, etc., or a mix of IGP and iBGP (which is involved because you could use a full-mesh, route reflectors, confederations, etc.).
What BGP neighbors send each other can be controlled. It could be full routing tables, or it could be whatever the AS owner decides is appropriate. there is no one answer to this question.
Best Answer
iBGP requires a full mesh or use of mitigation like confederations or route reflectors, BGP doesn't converge with anything like the speed of OSPF, etc.
Each OSPF router would have a full understanding of all the routes that are in the area in which it resides without needing a full mesh, and it converges very, very quickly.
Using an IGP is recommended with iBGP. Without the IGP, iBGP must neighbor on external-facing interfaces, with an IGP, iBGP can neighbor on loopback interfaces which never go down, and can have multiple paths to reach.
I have seen iBGP-only for local routing, but it is more difficult and fragile.