It seems that no part of Agrippa's or Domitian's Pantheon was still visible after the new building was errected. The Pantheon as we see it today is more or less a completly new structure. But that doesn't mean that no parts of the older buildings remain. Archaeological diggs from the 1890s revealed remains of a cirular wall of roughly 2 m hight that enclosed a space which was virtually congruent with the interior surface of the later Rotunda. They also found some of the foundations of a rectangular structure beneath the later Pronaos. Later work from 1996/7 unearthed the remains of the stairs that granted access to Agrippa's Pantheon and which were located more or less in the same spott as Hadrian's (or Trajan's) stairs. In combination those findings allow us to roughly reconstruct the Pantheon of Agrippa's times like this: The front on the north side comprised of classical temple fassade much like the one you're still seeing today. But this gave access to a circular courtyard that was open to the sky and limited by the 2 m high wall. This plan was seemingly later repeated with the building of Domitian. So the large domed Rotunda that can still be visited today was an innovation of the High Empire.

Nevertheless there might be another part of Agrippa's Pantheon left that can still be seen today. In a german article from 1997 Doris and Gottfried Gruben argued that the large bronze doors that connect Pronaos and Rotunda were in fact reused from the older building. They mostly base this on the proportions of those doors that don't really fit the dimensions of the wall in which they are incorporated. To my knowlege this hasn't really been proven or disproven yet but it certainly is an interesting thought.

As to your second question we can only speculate. While it might very well be that work on the third Pantheon already started under Trajan the building was certainly only completed in the time of Hadrian's reign. So it might be Hadrian's way to celebrate his own modesty in a really ostentatious manner by honoring the original donor with the largest inscription that the Roman world has ever produced. In the end the citizens of Rome still knew who in fact had provided them with this new temple.

As far as literature goes I highly recommend Kjeld De Fine Licht: The Rotunda in Rome. A study of Hadrian’s Pantheon (Kopenhagen 1968). He obviously couldn't incorporate the findings of the 1996/7 diggs so his reconstruction of Agrippa's Pantheon is quite different from the one I have described above. But his account of the archaeological findings up to this point is very detailed and very exact. For the newer reconstruction I can only point you to a very good article in german: Andreas Grüner: Das Pantheon und seine Vorbilder. In: Mitteilungen des Deutschen Archäologischen Instituts. Römische Abteilung. Band 111, 2004, S. 495–512. The other article I mentioned would be Doris Gruben - Gottfried Gruben: Die Türe des Pantheon. In: Mitteilungen des Deutschen Archäologischen Instituts. Römische Abteilung. Band 104, 1997, S. 3–74. They also didn't know about the findings of the newer diggs so their reconstruction isn't up to date but their handling of the archaeological facts they knew about still layed much of the groundwork for Grüner's later article.