I want to see if these features are specific to the browser version of QuickBooks Online. 

Please go to the following website, hover your mouse over Sign In, and select QuickBooks Online: https://quickbooks.intuit.com/. Once you're logged in, please follow the steps in the article above and let me know if you see those options this time around.

As for the payments service, this is required in order to accept the recurring donation. These payment accounts are set up as personal accounts, so I'm unable to recommend a person to enter in the business owner field. Whoever is selected will be held responsible for the account and will need to be the one to speak with support when it comes to discussing any account details, so perhaps someone from the board of directors can be chosen. This decision is completely up to the organization you're employed with.