To address the breadth of the question (US only) is slightly more complicated. The AIA provisions are in rule 37 CFR 1.290. There are other rules that relate to this.
The rules are all in a document called the MPEP.
MPEP 2204 Time for Filing Prior Art Citation [R-7]
Citations of prior art may be filed “at any time” under 35 U.S.C. 301. However, this period has been defined by rule (37 CFR 1.501(a)) to be “any time during the period of enforceability of a patent
This a different and older provision, the trick is this rule doesn't say anything about anyone at the USPTO looking at the documents. It still can be valuable to have it in the file.
Also there is a long standing rule that allows for a "protest" before the application is published. It might be used by someone the applicant threatened with an application on file as patent-pending.
1.291 Protests by the public against pending applications.
(a) A protest may be filed by a member of the public against a pending application, and it will be matched with the application file if it adequately identifies the patent application.
This never did much since it can't be used after the application is published.
Regarding other portions of the question: the phrase "bring prior art" is a little unclear. The examiner can search multiple times and issue multiple office actions rejecting the application on various grounds related to new references they find or new arguments they formulate. It is technically possible for an allowed application awaiting payment of the issue fee to be pulled back in the examination and give a new rejection. They are only supposed to do a new search when the applicant has made an amendment that necessitates it. In the normal course of events in the US the second rejection is nominally a "final" rejection but it is only final for the money you have paid them.
The applicant and everyone associated with filing and pursuing the application have a duty to disclose anything they know or become aware of that would tend have a negative light on the patentability or contradict a position they have taken. This continues until the day of issue. Regarding the applicant "dismissing" a prior art reference: they either need to show that due to dates or being from a "non-analogous" field it does not qualify as prior art or argue that it does not have all the elements of a claim, or amend one or more claims, etc.
Regarding the 9 month after grant time period. One, the Post Grant Review available in that time window is only applicable to first to file AIA patents of which there is currently one one granted. Two it is not a "send stuff in" thing. It is a very expensive very formal quasi-judicial proceeding.