These 2 questions are connected.  I’m assuming you’re using the Time Cards screens for time tracking and are not using Activities or Field Services Appointments for creating time records.

On the Time Cards screen, if you open up a posted time card, under the “more items” (...) button there is a “Correct” option so you can reopen historical time cards.  You can view this in the Help Documentation here: 2022 R2 Time Cards Help (the process is identical in the older versions)

The original time card will not change and remain as a “normal” type but will be hidden from employees.  A new time card will be created with the “Correction” type.  Then the time card can be edited as required.

Generally, anyone can correct any of their own (or anyone that they are a delegate for’s) time cards for any period.

If you want to restrict this, you can either just restrict access to the “Correct” button so that only a specific group of users can create the correction time card (i.e. your payroll group) or you can do a customization to restrict creation of correction time cards to the most recent time card weeks (i.e. only correct within the last month).

One thing that I have done to help with this at some of our clients is create a generic inquiry that flags any time on correction time cards that results in new billable hours or a change in total hours and built a business event to notify project accountants and/or the payroll group weekly so that they are aware of it (esp. if they are doing payroll outside of Acumatica or manually managing project completion percentages).