As you might guess, this article does not answer the questions. It does interview some archaeologists etc. and ask some more pretty good questions.
I suspect the Ark of the Covenant was melted down for its gold by the Babylonian conquerers. Jeremiah 3:16 implies it was already gone in Jeremiah's time. The Temple treasures may or may not have been evacuated and survived the destruction of Herod's Temple. If they did, they are likely irretrievably scattered and lost. But, naturally, there are proposals to the contrary.
For PaleoJudaica posts on the Ark of the Covenant, start here and follow the links. There are a great many posts, so many that it's hard to pick out key ones. Overal, I think, they cover just about every proposal about what happened to the Ark.
For posts on the Temple treasures, see here (cf. here) and many links. Some notable more recent posts are here, here, here, and again, follow the links.
The legendary Treatise of the Vessels (Maasekhet Kelim, not to be confused with the Mishnaic tractate), which tells the supposed story of the fate of the Temple treasures and the Ark after the Babylonian destruction of the Temple, comes up in these posts. For more on it, see here and links. I published an English translation of it in MOTP1.
The website of the Temple Mount Sifting Project is here. I have linked to it many times.
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