All the routers in an area will generate Type-1 LSAs to describe their directly attached links in that area. It doesn't matter if they are point-to-point links are not. Every router in an area will know about every other router and its links in an area.
An ABR will convert all the Type-1 LSAs in one area to a Type-3 LSA for the other area to which it is attached. The ABR Router ID will be the advertising router for the Type-3 LSAs which it generates. A Type-3 LSA can contain multiple networks.
From RFC 2328, OSPF Version 2:
When the LSA is describing a network (LS type = 2, 3 or 5), the
network's IP address is easily derived by masking the Link State ID
with the network/subnet mask contained in the body of the LSA.
What you quoted in your comment is actually on page 30, not 31. If you read it carefully, that area is performing a route summary, not to be confused with a summary LSA. You are confusing two different things. A Type-3 LSA is a summary LSA which contains all the networks for the Type-1 and Type-2 LSAs from an area. A summary route is a single, supernet route containing all the routes behind it. A summary route can only be advertised from an ABR in OSPF, but other routing protocols can use summary routes, and only OSPF uses LSAs.
Yes, they Type-3 LSA would contain all the individual Type-1 LSAs for all the routes covered by the summary route if the Area was not summarizing the routes, but the Type-1 LSAs themselves would not be leaked into Area 0.