Yes. the first one is a 500 and is a slant shank. While it can be used for FMQ, as per one of the links below, many find the thread path from the bobbin to the needle isn't the best for FMQ. There are several threads here on QB about the 500A and other slant shank machines that have lots of similarities to one another. There is a link
in one of the links below about a 401 and using 30W motor oil in the bearing to the motor, which would apply to this machine as well.
The other is, indeed, a 15 whose serial number was allotted in 1938. This is the machine which is frequently suggested to be a better machine for FMQ, as the the feed dogs can be dropped and the bobbin thread doesn't have to make a 90º turn to meet up with the needle thread. It takes regular low shank attachments.
Manuals for both machines can be found at
https://www.singer.com/support (Not affiliated with link).
As for cleaning the 15, especially, can be found at
How to Clean Up and use a vintage sewing machine - videos by Muv and Fav as well as other posts here in the vintage section.
Both are considered very good machines which can go to serve their original purpose for many years to come.
Should you do a search here on QB, the search function will not show the posts when you click on the links from the search result -
until you refresh the page. The page can be refreshed by clicking on the circle arrow next to the address bar or by clicking on the blue title of the thread above the first post of the thread.
Here are some of the links regarding the slant shank machines:
What Do I Need To Know About Singer 500A?
Free Motion Quilting on a Singer 500
Rocketeer needle and pattern selector problems
Differences between the Singer 500 and the Singer 503 machines
Janey - Neat people never make the exciting discoveries I do.