Hiya Chilly!
Austria-Hungary's ultimatum to Serbia following the death of Archduke Franz Ferdinand is handily translated and publicly available here. Additionally, Serbia's abbreviated response to the ultimatum can be found on the above hyperlink, or in full below. I unfortunately can't embed it due to bracket-use.
The only demand explicitly rejected by the Serbian government was that demand that:
"To take judicial proceedings against accessories to the plot of the 28th of June who are on Serbian territory; delegates of the Austro-Hungarian Government will take part in the investigation relating thereto;"
To which the Serbian government responded:
"...As regards the participation in this inquiry [which Serbia intends to hold] of Austro-Hungarian agents... [Serbia] cannot accept such an arrangement, as it would be a violation of the Constitution..."
Austria-Hungary's demands that its own police authorities be a direct part of any investigation was a thinly veiled threat. Austro-Hungarian investigators acting in the investigation would be there to ensure that its outcomes were desirable for the Austro-Hungarian government. Additionally, such involvement would have been a violation of Serbian sovereignty over its internal affairs, and would have effectively subordinated Serbian intelligence efforts to Austria-Hungary. In effect, it would compromise the investigation and turn it into a farce, as its findings would inevitably incriminate the Serbian government and provide a pretext for further demands.
The Austro-Hungarian ultimatum to Serbia was not designed to be accepted. It was designed to be effectively unfulfillable, and to provide Austria-Hungary with a casus-belli for an invasion. At the time, it was recognised absurd, and it was a sign of Serbian desperation that the document accepted in near-entirety. It was described by Edward Grey, the British foreign secretary, as:
"The most formidable document I had ever seen addressed by one State to another that was independent.”^1
Historical What-ifs are not permitted on this subreddit, so I won't be addressing the last part of your question directly. However, as I've explained above, the demands were designed to create future pretexts as appropriate. That Austria-Hungary was prepared to declare war because of Serbia's failure to meet just one of the series of extremely harsh demands demonstrates clearly that Austria-Hungary was negotiating in bad faith.
If you're interested, I've done a much more detailed write-up on the causes of the Great War here. Perhaps it'll help clear up any other questions. Otherwise, feel free to ask! :)
See you in Planetside, by the way. I'm home in just over a week, now!
Sources:
G.P. Gooch and Harold Temperley, British Documents on the Origin of War 1898-1914, Vol VIII (London 1926), p73
The demands boiled down to the Hague carrying out the investigation instead of the Austrians. A neutral party, as opposed to the party threatening Serbia with war. It was a sensible reasonable request, but ran into a problem: Austria had no intention of avoiding war with Serbia, and was going to reject whatever response the Serbs gave. They'd hoped that Serbia would reject the ultimatum, and it was meant to be rejected.