Great questions!
1] What organization is it?
The https://www.ourcommons.ca/ website is used by a part of the Parliament of Canada, and specifically, the House of Commons. For a legislative bill to become legislation (law) in Canada, two organizations of the Parliament of Canada, the House of Commons and the Senate, must each go through 3 of their own rounds of process. For each of these 2 organizations, as part of their respective third round, a majority of the respective organization must vote in support of the bill.
Even when these majority votes allow a bill to pass into legislation, it is possible that the legislation is great but it is also possible that the legislation is terrible, or somewhere in between.
The House of Commons represents the federally elected officials. It is also possible for a Member of the House of Commons not to be elected in certain circumstances, such as with Prime Minister Carney.
2] What is a petition all about and where does it appear?
As Charles mentioned, it is possible to submit a paper petition. This discussion will instead focus on electronic petitions but some of the information applies to either one.
https://www.ourcommons.ca/procedure/procedure-and-practice-3/ch_22-e.html "Petitions addressed to the House of Commons and presented to the House by its Members constitute one of the most direct means of communication between the people and Parliament."
https://www.ourcommons.ca/procedure/procedure-and-practice-3/ch_22_1-e.html "In Canada, provisions for petitions (long a feature of the pre-Confederation legislative assemblies) have always been part of the written rules of the House." Canadians have enjoyed the right to petition the House of Commons to comment on bills, legislation, or other matters affecting Canada, based not on the Constitution but instead based on well entrenched, centuries-old tradition and established precedent.
Practically speaking, petitions may fail to meet some requirements. If the petitioners do not want to abandon the issue, a petition will often have to be recreated. Improper language can be one reason. As another reason, 500 signatures are required before a chosen deadline. As another example, Parliament may get dissolved before a petition gets read and will need to be recreated in the following Parliamentary session. Some example petitions have been recreated 8 times, such as for repeatedly failing to meet the 500 signatures mark.
https://www.ourcommons.ca/petitions/en/Home/AboutContent?guide=PIElectronicGuide "Once the deadline for signing a petition has closed (i.e., after 30, 60, 90 or 120 days), the Clerk of Petitions will proceed with a final validation of signatures. If there are at least 500 valid signatures, the Clerk of Petitions will issue a certificate to the member of Parliament who authorized the online publication of the petition. It can then be presented to the House by any member. A record of this presentation will appear in the Journals for that day and the petitioner, supporters and signatories of the petition will be advised by email after its presentation."
"The Standing Orders of the House of Commons require the government to respond to every petition presented to the House within 45 calendar days. If the House is not sitting on that day, the response must be presented at the next sitting of the House. The petitioner, supporters, signatories, and the member of Parliament who authorized the online publication of the e-petition will be notified by email when the response is tabled in the House. A copy will also be found on the petitions website along with the original petition."
https://www.ourcommons.ca/procedure/standing-orders/Chap4-e.html "If such a petition remains without a response at the expiration of the said period of 45 days, the matter of the failure of the ministry to respond shall be deemed referred to the appropriate standing committee. Within five sitting days of such a referral the Chair of the committee shall convene a meeting of the committee to consider the matter of the failure of the ministry to respond."
3] Do these petitions actually do anything?
Petitions bring formal awareness of an issue to the Parliament of Canada and to interested members of the public. If this awareness leads to many people signing a petition or if the issue is of great importance, the media may report on the issue.
When the House of Commons responds, while it may not take the requested action, it will attempt to provide helpful guidance on the issue. Related laws or regulations may be quoted. Advice for contacting more relevant people may be given. For example, if a petition was made to the House of Commons for educational reform, the House of Commons may suggest contacting provincial and territorial governments since it is those governments who look after education matters in Canada.
When it is in the power for the House of Commons to directly act on an issue, it is possible for a related action to take place.
4] What happens to my information?
The person who initiates (creates) a petition has their name, city, and province or territory published on the House of Commons website. This person should truly believe in the worthiness of the cause and should be willing to stand up for the issue being raised. If it is a truly noble, worthy, and appropriate cause, this person deserves our respect.
https://www.ourcommons.ca/petitions/en/Home/AboutContent?guide=PIElectronicGuide "The petitioner's other personal information will be safeguarded on the House of Commons' servers."
The personal information of an initiator, a supporter, or a signatory may be used to contact that person by the "House of Commons' authorized personnel" during the petition process. For example, email addresses will be used for validation and phone numbers may optionally additionally be used for validation. "Data may be used for statistical purposes."
"None of the personal information provided to the House of Commons by a supporter or a signatory will be published on this website."
"a general breakdown of signatures by province and territory will appear and remain on the website along with each e-petition."
"Supporters' and signatories' personal information collected through the petitions website will be safeguarded for a duration of six months after the e-petition becomes inactive, or until the dissolution of a Parliament, whichever is earlier, after which it will be destroyed by the House of Commons' authorized personnel."
5] Guidance on inappropriate petitions
A petition should not include signatures from fake people and should not contain information known to be false. A petition should be cautious not to include potentially libelous or defamatory statements.
A petition should not be about "impertinent or improper matters" and it would likely be better to vent about these things on social media than to waste valuable time in Parliament, since a relevant action will not be able to take place.
My best guess would be that a minimum of five supporters helps to weed out some inappropriate petitions. Having more than five can help to meet the minimum in certain circumstances, such as someone falling critically ill and not being able to participate any longer. Having more than ten could create an additional administrative burden.
Supporters are expected to be valid people, actually be in support of the petition, and be responsive to email.
If we could provide more than 10, imagine what might happen. If 2000 people were allowed, those people might just be people from the initiator's address book who know nothing of the issue. The burden would fall on the House of Commons to poll each person until 5 of them agreed to the petition. With the realistic limits, the initiator is expected to be sufficiently serious and responsible about the petition process.