Is there a connection between the Court and dark, poorly ventilated interiors?

There seems to be. You may arrive at your own conclusions of metaphor or symbol, but the relationship at least is fairly consistent. The meeting hall of the first interrogation is dim and hazy. The atmosphere of the law offices is suffocating and sends K. into collapse. The Whipper whips the warders in a wood closet. The Court's painter lives in an insufferably stuffy attic. K.'s consultations with the lawyer take place in the latter's darkened sickroom. Even the cathedral, where K. meets the chaplain, is virtually pitch black due to the storm brewing outside. All of this can have a profound effect on the reader, who may feel herself as confined by the descriptions of these interiors just as by the stonewalling of the Court or K.'s obdurate inability to see the danger he's in.

Is K's inability to "think outside the box," his susceptibility to being drawn into the process of the trial, the basis of his eventual guilt?

Kafka invites you to ask such questions, and lets them stand without answer. Could K. have survived if he had simply gone away? Could he have wanted more to prevail? The question is open. "Logic is doubtless unshakable, but it cannot withstand a man who wants to go on living," K. says to himself, moments before he is killed. And yet, whatever we determine to be the state of K.'s will, Kafka also shows us that will is not enough. Consider the opaque yet radiant parable of the man who asks admittance to the Law. Certainly that man does not lack will--he expends his life in his will to encounter the Law, though he is apparently free to abandon his quest and simply walk away. But abandonment of the Law, of Logic, is abandonment of justice, of dignity, of personhood. It may constitute thinking outside the box, but it is also a retreat (and to where?). Besides, nowhere is it stated that K. can merely abandon the Court, that the Court excuses those who fail to be drawn into its web of doubt, pandering, and self-recrimination. We do not know the Court's jurisdiction. There is neither a clear way out nor an unequivocal indication of doom until doom is at hand. In this light, blaming K. for his own demise is analogous to blaming victims of the Nazi death machine for not perceiving in advance the full trajectory of depravity, or blaming Stalin's victims--who never had the option of stepping beyond the purview of a perverse Law--for their fate.

To what extent does K. believe that he is guilty?

We are not given clear indications. One thing is certain, though: K. is expecting someone to come for him on the morning of his thirty-first birthday. He perhaps hopes for someone other than the two clowns who show up, but he nonetheless is expecting an emissary. Since he is expecting someone and seems to know roughly what is going to happen, and since he has not made an attempt at escape or any final defense, he appears to have accepted the verdict. As the prison chaplain remarked, "it is not necessary to accept everything as true, one must only accept it as necessary." Perhaps K. accepts his execution not because he believes he is truly guilty, but because--and what is more shameful--he accepts the Court's argument that it is necessary.