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Chametz that is stuck onto a wall or vessel:

Chametz that is stuck onto an item [utensil, chair, and table]-Letter of the law:^[1]

Chametz is loosely stuck: A piece of Chametz which is being loosely held in a vessel, such as if it has fallen into a crack, needs to be destroyed even if one nullifies it before Pesach, unless it is less than a Kezayis and is dirty enough to be considered inedible.[2]

Chametz is stuck: If the Chametz is stuck to the vessel, then if within the entire vessel there is less than a Kezayis of Chametz, then it does not need to be destroyed, and rather it suffices for one to nullify the Chametz before Pesach.^[3] However, if it was not nullified before Pesach, then it Rabbinically needs to be destroyed.^[4] Likewise, if within the entire vessel there is a total of a Kezayis or more, then one must destroy the Chametz even if its stuck to the vessel [and will nullify it before Pesach].[5]

Chametz based sealant that was used to seal a hole in a vessel:[6] Those areas of sealant which are less than a Kezayis do not need to be destroyed, if one nullifies the Chametz before Pesach. This applies even if within the entire vessel there is a total of a Kezayis or more.[7] [If it was not nullified before Pesach, then it Rabbinically needs to be destroyed.^[8]] However, those areas of sealant which contain a Kezayis of Chametz must be scraped off, or covered over with cement, before Pesach.[9] This applies even if one will nullify the Chametz before Pesach.

Chametz stuck to walls-Letter of the law:^[10]

Chametz which is stuck to a wall follows the same laws as Chametz stuck to a vessel, and hence must be destroyed if it is a Kezayis in size or was not nullified before Pesach.[11] If, however, it is less than a Kezayis in size, and [was or] will be nullified before Pesach [in Kol Chamira], then it does not need to be destroyed. If there is a total of a Kezayis of Chametz throughout the walls, floors, or ceiling of a single room, then the Chametz is Rabbinically viewed as a single Kezayis piece and must be destroyed.[12] 

Chametz based sealant that was used to seal a hole in the wall:[13] [In previous times it was common practice to use a flour-based sealant to seal holes in a wall. Some people practice this until this very day. The following is the law regarding a Chametz based sealant:] Those areas of sealant which are less than a Kezayis do not need to be destroyed, if one nullifies the Chametz before Pesach. This applies even if within the entire room there is a total of a Kezayis or more.[14] [If it was not nullified before Pesach, then it Rabbinically needs to be destroyed.^[15]] However, those areas of sealant which contain a Kezayis of Chametz must be scraped off, or covered over with cement, before Pesach.[16] This applies even if one will nullify the Chametz before Pesach.

The Custom-Yisrael Kedoshim Heim:^[17]

All the above is from the letter of the law, however practically, the Jewish people are holy [i.e. Yisrael Kedoshim Hem] and are accustomed to be stringent upon themselves and scrape off every speck of Chametz that is stuck to the walls [ceiling or floor] or vessel. They are even furthermore stringent to sand down the benches and chairs and walls which touched the Chametz. [Hence, due to this custom, one is to destroy all Chametz that is stuck to one’s wall or vessel, even if from the letter of the law it is not required to be destroyed.] One is to scrape off whatever Chametz he can and whatever he is unable to scrape off, one should cover over with cement [or pour bleach or another spoiling agent over it].[18]  

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^[1] Admur 442:28

[2] If it contains less than a Kezayis then it only needs to be destroyed Rabbinically. If it contains a kezayis or more than it needs to be Biblically destroyed if one did not perform Bittul. [Admur ibid] Vetzaruch Iyun if all the loose crumbs in a vessel join to form a Kezayis, and are hence Biblically required to be destroyed, as explains Admur 442:29. We find a precedent regarding hafrashas Challah, that loose bread can join to form Shiur Challah if they are all in one vessel.

^[3] Admur 442:28

The reason: as since its stuck to the vessel its nullified to the vessel and thus does not need to be destroyed

^[4] Admur 442:29

The reason: This is as a safeguard against coming to own a Kezayis worth of Chametz. [Admur ibid]

[5] Admur 442:28

The reason: As all the Chametz in the vessel is Biblically considered to be joined together to form a kezayis. [Admur 442:29]

[6] Admur 442:27

[7] The reason: As the Chametz is considered nullified to the vessel and are considered to be part of its walls. [Admur ibid]

^[8] Admur 442:29

The reason: This is required as a safeguard against coming to own a Kezayis. [Admur ibid]

[9] The reason: As since it is a size of importance, it is thus not nullified to the vessel and is thus not considered to be part of its walls. [Admur ibid]

Two half zeisim attached with a dough string: If the dough string is sturdy enough to drag with it the two half zeisim pieces, then it is all considered one Kezayis and must be scraped off. [Admur ibid]

^[10] Admur 442:29

[11] Even by less than a Kezayis piece, if it was not nullified before Pesach it Rabbinically needs to be destroyed completely from the world, as a safeguard against coming to own a kezayis worth. [Admur ibid]

[12] The reason: The Chametz that is attached to the walls of a room does not Biblically join together to form a Kezayis, and thus Biblically it suffices to nullify the Chametz before Pesach. However, Rabbinically, all the Chametz that is stuck on the walls/floor/ceiling of one room [join together to form a Kezayis as] at times they are swept together and become joined. Thus, one must destroy the Chametz even if he plans to nullify it before Pesach, [unless it is placed on the wall as a sealant to fill up holes or cracks.] However, the Chametz of two different rooms do not join to form a Kezayis, and thus if one has only a half Kezayis in each room he does not have to scrape it off, if he will do Bittul before Pesach.[ [Admur ibid]

Chametz attached to a window: Chametz that is attached to a window does not joined together to form a kezayis because the window is attached to a wall and a wall does not join together to form a Kezayis. [Admur 442:25] Vetzaruch Iyun, as here Admur states that Rabbinically the Kezayis does join even by walls. Perhaps however one can say that by a window we do not assume that it will be swept up and join to a Kezayis, and hence the sages did not decree against it.

[13] Admur 442:27

[14] The reason: As the Chametz is considered nullified to the vessel and are considered to be part of its walls. [Admur ibid]

^[15] Admur 442:29

The reason: This is required as a safeguard against coming to own a Kezayis. [Admur ibid]

[16] The reason: As since it is a size of importance, it is thus not nullified to the vessel and is thus not considered to be part of its walls. [Admur ibid]

Two half zeisim attached with a dough string: If the dough string is sturdy enough to drag with it the two half zeisim pieces, then it is all considered one Kezayis and must be scraped off. [Admur ibid]

^[17] Admur 442:30; Michaber 442:6 “The custom is to scrape the walls and chairs which touched Chametz and they have upon whom to rely”; Tur 442; Rosh 3:2 “I did not lengthen on these laws of dough stuck on vessels as the Jewish people are holy and are accustomed…”; Raavan, brought in Rosh ibid “This custom of scraping down the walls and chairs has a root in the Yerushalmi”; Rokeiach 247; Radbaz 1:135 “The Jewish people are holy as writes the Rosh, and as we see that they keep extra Chumros, in contrast to other Issurim”; Yosef Ometz 699; Mamar Mordechai 442:6, M”B 442:28, Kaf Hachaim 442:69 “Since the custom is based on the Yerushalmi, one is therefore not to belittle it and claim it is a Minhag Shtus and superfluous stringency.”

[18] Admur ibid; Michaber ibid; From the letter of the law however, it is permitted to leave the Chametz there throughout Pesach, so long as one plans to do Bittul. [See Admur 433:19]