Why are torture chambers so damn common in historic sites/castles/museums all across Europe?

How much do these exhibitions misrepresent the reality of torture in the Middle Ages and the Early Modern Period?

I will answer this part, limiting myself to the Spanish territories, as they are the ones I know in reasonable depth.

The misrepresentation is comically monstruous. None of the things you see are devices ever used or conceived by the Spanish Inquisition, or even the civil justice system, some of the implements are not even torture devices but execution instruments such as the extremely famous guillotine. So, back in order, what elements did the Spanish Inquisition and the civil justice use in Spain?

-The strapado, known in Spanish as "garrucha". It is a pulley, a rather simple one. The accused or the witness would tied with his hands behind the back, and raised with a pulley that would make the upwards traction from that knot behind the back. A weight was placed in the accused's ankles, to make the torture more effective.

-The rack. This one is very famous, a peculiar contraption that would partially dislocate the joints of the shoulders and the ankles.

-The handkerchief or waterboarding. This method was made awfully famous by the CIA and the American army in Guantánamo. The ministers of the torment would forcefully insert a handkerchief or piece of cloth down the accused or witness' throat, and the start pouring water. This would simulate asphyxiation.

One has to bear in mind that the Inquistion was not allowed to draw blood or cause any permanent or lasting damage on any person, and doing so would result in the annulment of the cause. Furthermore, the Spanish Inquisition did not trust the efficacy of torture for extracting confessions, and I cannot explain it better than the Inquisition's own procedural rules, articles 49, 50, and 53:

49. [...] Experience teaches us that the accused, in that agony, would confess anything that is suggested to them, which causes damages to third parties, and occasion for their confessions to be revoked.

50. The Inquisitors shall carefully examine whether the sentence of torment is justified or not, and preceded by legitimate evidence. In case they have issues with this, or doubts, as the damage could be irreparable, for in cases of heresy interlocutory sentences can be appealed, shall then the appeal be granted. [...] When in doubt, appeal shall always be granted. Also, the sentence of torment shall not be executed until the cause is concluded, and having received the accused's defendants.

53. Twenty four hour having passed after the torment, the accused shall ratify his confessions, and in case he revokes them, he shall be repaired as provided by the Law.

The civil justice had these same methods, and we have some strange literary evidence coming from Juan de Arce de Otálora, a judge from the mid 16th century, and a very illustrious one. He was president of the Hall of Criminal Matters of the Real Audiencia y Chancillería de Valladolid, the highest court north of the river Tajo. In his Coloquios de Palatino y Pinciano, we find this little gem:

PINCIANO- The better I have dinner, the better I sleep, in accordance to the text that says "fill me up, lay me down, and if I don't sleep, kill me". And in the days of fasting, if I don't have a roman collation, I can't sleep. And some times after dinner fights me so hard, that were it disturbed, it would be so hard a torment upon me that would I confess any felony, same as the sorceress that Hyppolitus mentions, who after having been administered the toque, and the strings, and the strappado and having not confessed, had her fed for good and sat down on a bench between two persons that would not allow her to sleep, and who would wake her up when she tilted her head; and he says that after forty hours she confessed

Ippolito Marsili, the Hyppolitus mentioned by Arce de Otálora does not mention using the toque, the strings, and the strappado, but the usage of all available methods. Otálora, being a Spanish judge, adapts what Marsili said to his own practices.