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Interesting, indeed.  What you have here is a library's "descriptive catalog" for the Leake Family Papers—i.e., a guide to the collection. As is common with a large collection about a person or a family, it begins with a biographical sketch, then briefly identifies each numbered item in the collection.  

I did not read every page of this lengthy two-part guide but, in scrolling, I did not see where any of the actual family papers are online. Therefore, if you use anything from this two-part guide, you are not using the actual family papers, you are only using the library's descriptive guide.

The complicating factor here is that Parts 1 and 2 are sub-pages (files) linked under the main page that is found via your third URL. The simplest approach would be to cite the main page, then (depending upon whether you need to cite Part 1 or Part 2) cite the subfile as a waypoint, followed by the specific item of interest.  For example:

“Reference to Index of Papers of John Leake (1780–1865) of Rosedale, near Campbell Town,” descriptive catalog, University of Tasmania Library, EPRINTS (https://eprints.utas.edu.au/10860/ : downloaded 5 May 2025) > PDF Part 2 , p. 1, JOURNALS, item H.80,  “C.H. Leake’s Journal 17 Feb. 1839 – 6 June 1840,” which references “Mr. Oakden who is going to be married.”