I'm most curious about the success rate of sieges of medieval castles, before the usage of gunpowder weapons, but if you know about sieges of fortified cities in antiquity then please do chime in!
I know it can be kind of a broad question, what with all of the different armies and castles out there, so interpret it as an "in general". The median castle, stocked as a castle normally would be when they were at war, confronted by the median army with orders to take the fortification.
The only tricky part is this: no help is coming for the castle/town, and the besieging army is not being recalled for use elsewhere (I do know that your army wouldn't always be available for a long haul siege, but this army is). If the besieging army feels they must take the point by storm, it's only because the siege is becoming untenable due to starvation, harassment from sallies, losses to disease, or other such factors.
So, how many of these nondescript castles can outlast their nondescript enemies?
The only tricky part is this: no help is coming for the castle/town, and the besieging army is not being recalled for use elsewhere (I do know that your army wouldn't always be available for a long haul siege, but this army is). If the besieging army feels they must take the point by storm, it's only because the siege is becoming untenable due to starvation, harassment from sallies, losses to disease, or other such factors.
No, sorry. This is explicitly not the tactical or strategic purpose of castles.
Castles allowed a relatively small garrison to hold down an invading army until a larger force could arrive, thus allowing a lord to protect his territory. Thus, the situation you describe almost never happened, and certainly not with enough regularity to make any sort of general statements.
A castle was a massive investment of resources in terms of materiel, man-hours, and coin. They were only constructed because they worked very well, and were thus a worthwhile investment. Most sieges failed, and they failed because the castle performed its strategic purpose - it held long enough to be relieved.