You've posted to the FM GO Forum. Is this in context of doing it all on an iOS device such as an iPhone or iPad? Or did you intend to post to the FM Pro Forum? (See the tabs at the top of your screen)
Either way, it is possible to do most of this if you design your database to support it. Add a date field to your table, ModDate and use field options to specify that the modification date be automatically entered. Now, any time a record is created or edited in any way, the date in this field will update to record the current date.
You can then perform a find for all records where the date in the ModDate field are in the range of dates (such as last weeks dates) you specify. You can do this manually or in a script.
What this won't tell you is how the data was changed only that it was edited in some way. If you want to know exactly what fields were modified and what the previous values were in those fields, this is also possible but takes a great deal of scripting to set up as you'd need to use script triggers on all editable fields to capture and log previous field values before the user edits them.
Create a layout using the Report option and make the choices for your style of report. Use Phil's idea or some other to create the selection of records. You can assign the sort to be remembered.
Now you just find your selection of records and use the layout.