Second - I have a square store, but I can't seem to link to my specific items within my square store with the items in my square library.   Also, I'd

Second - I have a square store, but I can't seem to link to my specific items within my square store with the items in my square library.   Also, I'd like a way for "Products" to allow a selection of payment for cash (paid to specific place) and check to be mailed.  

Sorry, I'm not quite sure what you mean with "link to specific items within your square store". I'm afraid that's not possible in the square payment field.

With regards to the check payment, you can add products in your form with zero price and indicate in your product description the actual price of the product. So when the form is submitted, the user won't be charged and the form would submit right away.

Example:

You can also setup square payment along with check payment through conditions.

Here's a similar guide for that: https://www.jotform.com/help/120-How-to-Set-up-Paypal-Along-with-Other-Payment-Options

Hope this helps!