Can the player prevent the construction of alien bases?
Yes, by religiously intercepting UFOs that are going on base-building missions.
What happen when a base is destroyed, but has spread XVI in the immediate area? The spread slows... the XVI dies out... or nothing?
The spread retreats somewhat, particularly if the player has an effective anti-organism researched, but it won't be possible to wipe it out completely. Also, infected areas without alien bases will try to link up with the nearest base(s).
Is the player actually able to stop the XVI or is it an inevitable part of the story-line?
The player will be able to slow XVI spread through research, interception and tac missions, but it will eventually take over the whole planet unless the player reaches and performs the final campaign mission.
If the player can cure an infected area... how does he do that?
There's no way to fully cure an infected area.
How does XVI infection relate to the 8 nations paying the bills?
PHALANX efforts or failures to fight XVI spread have a high effect on nation happiness. When infection rates in a region exceed 50%, the nation will start to contribute less and less money to PHALANX. At some point between 70% and 90%, the nation will cease to contribute completely. After 95% the nation becomes actively hostile to PHALANX.
The figures are adjustable, but they get the basic idea across.
Regards,
Winter