Regarding property, land owned by people who were expelled, left, or were otherwise displaced during the war was transferred to the Custodian for Absentee Property, an Israeli quasi-governmental agency. This land was then essentially handed over to the government over time.

It's important to note that Israeli property law is an intractable mess, because it's a hodge-podge of Ottoman law and laws from the British Mandate. The Israeli government owns nearly all land in Israel--when someone buys land from the government they are invariably receiving a lease of indefinite length. Anyway, Ottoman property law divides land into several categories, and land which is sorta-government controlled (kinda like Israeli leases, not coincidentally) had to be cultivated for the "ownership" to be maintained, which is actually a lease under terms quite like private ownership. The result is that by not allowing Palestinians to return after thew war, the land could be seized using existing legal framework.

Wikipedia goes through the various Israeli laws involved. This essay is a brief bit of writing, summarizing "The Land System in Palestine — History and Structure" by Abraham Granott, which talks about ottoman law. If you have JSTOR, this seems interesting.

As for attempts at addressing it, the Lausanne Conference in 1949 was probably the best shot. Israel agreed in principle to repatriation of many refugees and compensation for property, but was only willing to do so as part of a comprehensive peace agreement. That wasn't a realistic prospect at the time, so nothing came of it.