Find function: yes.
paper type: Maybe
Open Manage | database | Relationships and note the boxes you have there. Each of these boxes is called a table occurrence as you can define more than one occurrence of the same table. Each table occurrence has it's own found set, current record and sort order.
Thus, one way to produce a new found set that does not affect the found sets shown on other layouts for the same records is to click the table occurrence box and use the duplicate button (two green plus signs) to create a second occurrence of that table. If you base a layout on that new occurrence by selecting it in Layout setup... | Show Records from, the found set on that layout will be independent of that found on layouts based on the original occurrence.
For more on table occurrences, you might see this tutorial: Tutorial: What are Table Occurrences?
Printer settings are global to the entire file, but you can use scripts with either Print or Print Setup to specify specific printers and settings. However, users have complained that some printer settings--such as paper size weren't being retained by the print setup script step so you will need to test with your copy of FileMaker to see if it works for you or not. (An OnLayoutEnter trigger can perform a script that includes the print setup step to specify options for the current layout.)