Start by looking at the GROUP BY - you have far, far too many clauses in there, which is why you get more rows than you want. (This may help you understand why: SQL GROUP By and the "Column 'name' is invalid in the select list because..." error
So start with a simpler GROUP By:
SELECT AucNumber, MAX(BiddingPrice) AS MaxBP
GROUP BY AucNumber
That won't return you all the info you want, but it should bring it down the just the rows you want.
Then, use a JOIN to combine that with the rest if the data:
SELECT a.* FROM AuctionsSelectedNumber
JOIN (SELECT AucNumber, MAX(BiddingPrice) AS MaxBP
GROUP BY AucNumber) b
ON a.AucNumber = b.AucNumber AND a.MaxBP = b.MaxBP
I don't have your test data, so I can't check it - but that should do what you want.
If it doesn't, show your input and output data, and explain where the output is wrong.