Could an amendment be passed which abolished the Senate entirely (or reduced its powers to serve purely ceremonial functions) and created a new house of Congress with identical functions but excluding one particular state, without that state's consent?
There could be an intricate way of doing that, by first amending the constitution to remove or nullify the final clause of Article V, and then amending the legislative branch. That's discussed here : https://law.stackexchange.com/a/83576/36903
But the way your question is asked, no, it seems very unlikely that a constitutional amendment could directly deprive (in effect) a state from representation in the upper house of the US legislative branch without being censured by the courts.
A different version depriving the Senate of (most if not all of) its powers, and adding a third House and vesting it these powers, could possibly have better chances of withstanding a challenge by the judicial system, because any state would not see its equal representation in the Senate diminished. But that's going far in the hypothetical.
One can argue both ways. On one side, yes, zero representation in the Senate for all states is equal suffrage in the Senate. On the other side, no, depriving all states of all representation in the Senate deprives them of their suffrage in the Senate (without needing to consider the question of whether the suffrage is equal).
Since this question has never been considered by a court, we can't do much more than speculate how one might rule. There has never been an amendment proposed to modify the composition of the Senate -- at least not one that was seriously considered.
The spirit of the law works in favor of the second interpretation. Furthermore, a strict application of abstract logical reasoning was probably not the intention of the framers.
A strategy that might seem more likely to succeed would be to introduce amendments reducing the Senate's power in the legislative process, similar to the evolution of the House of Lords in the UK.
If the goal were to sideline one state, this might work, but if the goal is to address the complaint that the Senate is undemocratic because people in smaller states have proportionally more influence there, there's no way the amendment would pass 3/4 of the states' legislatures. The number of states with one or two representatives is 13, by itself a sufficient number to block the adoption of an amendment.
Could an amendment be passed which abolished the Senate entirely . . . and created a new house of Congress with identical functions but excluding one particular state, without that state's consent?
While this has never presented itself and there is always uncertainty as a result, probably not. This would abridge the equal representation in the Senate clause.
Could an amendment be passed which . . reduced [the Senate's] powers to serve purely ceremonial functions . . . ?
Probably so, and particularly if it wasn't purely ceremonial but instead had its powers reduced to those of a house of revision like the U.K. House of Lords, or the Canadian Senate.
For example, a constitutional amendment providing that a law could be passed by any of the existing methods but also by approval by the U.S. House, followed by inaction by the U.S. Senate on the U.S. House bill within six months or reject of the U.S. House bill, followed by reapproval of the original bill by the U.S. House and a signature by the President, might very well be constitutional.
Similarly, a bill transferring responsibility for approving Presidential nominations from the U.S. Senate alone to the U.S. House alone, might be constitutional.