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Every Jew, man or woman, who will be living in a home over Pesach, is obligated to clean and it for Chametz and perform a Bedika. Furthermore, even if he will not be living in the home over Pesach, he is obligated to clean and check all of his property for Chametz, unless the property will be sold to other people over Pesach, as explained in Chapter 3 Halachas 12-13-See there! If one does not own a home [see next regarding household members], he is exempt from this Mitzvah.
One who is traveling away for Pesach: One who will be away from home for the entire duration of Pesach is exempt from cleaning/checking his home prior to leaving if he will be performing Mechiras Chametz. Nevertheless, if one will only be arriving to his destination on Erev Pesach [i.e. the 14th of Nissan], then it is proper for him to clean at least one room and perform the Mitzvah of Bedika at home on the night of the 14th, or the night prior to leaving. See Chapter 3 Halacha 12 A-B and Q&A for the full details of this matter!
Who in the household does the obligation fall on?
The obligation to check the home for Chametz falls upon the father/master of the home, and not upon any of his [family members and other] dependents. However, in a case that the owner is not at home to do the search, then the obligation falls upon the dependents [even if the father did not directly appoint them to do the search].
If one lives in the house of another Jew does he have to also search for Chametz? One who will be living in another’s home over Pesach, is not required to perform his own individual cleaning and Bedikas Chametz if the owner of the home will anyways be doing so. [This applies even if one purchases and eats his own Chametz in the home.]
Who is responsible to check and nullify the Chametz of orphans? The caretaker of the orphans is obligated to check and nullify the Chametz of the orphans just as he is obligated to do for them all the other Biblical and Rabbinical commands.
If the dependents have their own money which they use to buy food are they also obligated in the Bedika?
Yes. However, in such a case the dependent receives the same status as one who lives in the house of another Jew, in which case the house owner fulfills the Bedika obligation on behalf of the Jew.
If the father is not at home, are the dependents obligated to check the house with a blessing?
If one is living in the house of a gentile, does he have to check the gentile’s house for Chametz?
If the gentile is the owner/master of the home then he is to simply nullify and disown his Chametz, and let the gentile know that it is all his, and he may take it for himself. However, if the Jew has his own room within the home, then certainly he is obligated to check his personal room with a blessing. Although it is seemingly permitted to live in the home of a gentile throughout Pesach even though the gentile will have Chametz in the home, nevertheless, it is best to avoid doing so.
Who is responsible for searching for Chametz in the stairs and lounge of an apartment building?
All the residents have an obligation to search their building for Chametz. The building residents should appoint one person to do so and thus fulfill their obligation.
Who is responsible for checking a Yeshiva, or school for Chametz?
The responsibility falls upon the directorship of the institution. If they do not plan to use the premises during Pesach, they can simply include it in the sale to the gentile, and thus avoid the need to clean it out. If, however, it will be made use of during Pesach, then it must be cleaned.
Who is responsible for checking a school dormitory for Chametz?
Each student is to check his room for Chametz prior to leaving, unless the room will not be used during Pesach, and both he and the directorship of the school perform Mechiras Chametz. The remainder of the building is the responsibility of the directorship to clean, as stated in the previous Q&A. Regarding if a student may recite a blessing upon checking for Chametz in his dorm room on the night of the 14th, some Poskim rule a blessing may not be recited. Other Poskim rule a blessing may be recited. Practically, the student may recite a blessing upon searching on the night of the 14th.
 Admur 432:8; 436:3
 The reason: The reason for [why the dependents are not obligated when the father is around] is because the Chametz in the home belongs [only to the father/owner of the house and] not at all to any of the dependents. [Admur 432:8]
 The reason: When the father is not around, the dependents are obligated to clean and search the home not because they will transgress an owning prohibition, but rather Kol Yisrael Areivim. Meaning, that since the homeowner was obligated to search for Chametz all the rooms which are required to be searched [as explained in chapter 433] therefore, those who remain in his home are obligated to exempt him from his obligation, as all Jews are guarantors for each other. [Admur 436:3]
 Admur 436:20
 The reason: If one will be moving in with someone else, and that someone else is the owner of the house, and that owner will check for and destroy the Chametz himself [and thus he will not be able to do a Bedika for Chametz], nevertheless, since the owner will also search and destroy the Chametz which he [the guest/boarder] used in that house from when he arrived there until Pesach, therefore, this owner is considered to be his [the guests] emissary to check and destroy his Chametz. Now, since the rule is that the emissary of a person is like himself, therefore it is considered as if he himself has destroyed his Chametz, [and he has thus fulfilled the decree of the sages to search for and destroy the Chametz of at least one home, no matter what the situation]. [Admur ibid]
 Admur 434:16
 See 436:20
 Although they are not obligated to search the house due to of Baal Yiraeh, and are only obligated to search it because of Kol Yisrael Areivim, in order to fulfill the fathers obligation of the search, nevertheless seemingly a blessing is said being that we consider the household members to be the emissaries of the father, as zachin liadam shelo bifanav. Therefore, a blessing is said, just like when any emissary is appointed to do the search.
 See Admur 436:20
 From the letter of the law it is permitted to do so, as one does not own the Chametz anymore [as explained in Admur 436:20] and in such a great case of Hefker to the gentile, there is not even a Rabbinical obligation to clean the home [as explained in Admur ibid]. Furthermore, although even the Chametz of a gentile must be placed behind a Mechitza lest he come to eat it [Admur 440:5], this is only required in one’s own home, when the gentile is not there. However, when living in a gentile’s home, in presence of the gentile, we do not suspect that one will eat from his Chametz unless one is eating with him the same table. [See Admur 440:3-4] Nonetheless, this is certainly not an ideal situation, and hence one should do all in his power to make other arrangements for Pesach.
 Piskeiy Teshuvos 433:3
 See Teshuvos Vehanhagos 1:287; Moadim Uzmanim 3:287; Chovas Hadar end of Sefer; Piskeiy Teshuvos 437:3
 The reason: It is debated amongst today’s Poskim as to who is responsible for cleaning the dorm rooms for Chametz, and if it’s similar to a rental or not. Some say it is the responsibility of the student, as he pays tuition to stay there. [Piskeiy Teshuvos 437:3] Others say it is the responsibility of the directorship, as they own the place and have the right to move students from one room to another, and it is hence not a true rental. [Teshuvos Vehanhagos 1:287; Moadim Uzmanim 3:287; Chovas Hadar end of Sefer] Accordingly, the room may not be left unchecked unless both the student and directorship include it in their sale contract in order to cover all opinions.
 Teshuvos Vehanhagos 1:287; Moadim Uzmanim 3:287; Chovas Hadar end of Sefer; Piskeiy Teshuvos 437:3
 The reason: As the students do not own their dorm rooms at all, not even as a form of rental, being the directorship have the right to move students from one room to another, and it is hence not a true rental. Accordingly, the checking obligation falls upon the institution and not the individual students who are merely considered like members of the household of the institution. Thus, only one blessing may be recited upon checking the entire dorm, and not one blessing per student or per room. [Teshuvos Vehanhagos 1:287; Moadim Uzmanim 3:287; Chovas Hadar end of Sefer]
 Piskeiy Teshuvos 437:3 in name of Chazon Ish; Implication of Admur 436:20 that a guest who eats his own Chametz is considered to have his own individual obligation to check for Chametz, and is not viewed as a household member or dependent [brought in 432:8] who does not own the Chametz and does not have an individual obligation. Now, Yeshiva students pay tuition and hence have in truth purchased their meals. Accordingly, there is no reason to not consider the Chametz as theirs, and therefore they may choose to recite a blessing upon making the search.
 The reason: As the rooms are considered owned by the students, being they pay tuition for room and board. [ibid]
 As so is implied from Admur ibid