Pretty easy tho you most likely need to use a web browser. 

 So, to that, I would say to enter it when you write it, so that you and YNAB know that it has been “spent”. you could theoretically, with a regular bank register, move it to when it actually went out, but that might affect your YNAB budget history so I would advise against it

 it’s not really money to you until you cashed or deposited it, so I will probably just do the date that you did so

No, because you don’t have a online login for the backend bank.

I’ve had a mint.com account for years so I just use that. View the account, export the new transactions, and import into YNAB

This type of detection isn’t great for immediate response but espresence does let you use various sensors with it to detect the initial presence (motion, light, and a few others)