Is it possible to have Google Sheets remember each user's either last cursor location or last edited cell or preferably the value of the cell in Row2 that matches the current date? (In Row1 I have the day of the week that corresponds to the date that is in the same column but in Row2.) And then when each user opens the spreadsheet, their cursor will automatically go to that saved location. Is this possible?
To make Google Sheets "remember" something like the last cell edited by each user first you could use a on edit or on change Google Apps Script triggers to get the cell address.
To make Google "remember" the value of a cell, as the value could be volatile, then you should use a Google Apps Script time-driven trigger or if you only require the last value shown to a user, then you could use an HTML Service dialog or sidebar and client-side code to poll de cell value every second or something like that to get the value.
Once your script has the cell address or value, your script could store it somewhere like a sheet in the same spreadsheet, the Properties Service as a script, document or user properties or an external resource.