I appreciate for being detailed about the issue. I can help point you in the right direction in integrating QBO to the POS applications mentioned.
For Square, you’ll have to use their merchant account and connect it to QBO. This way, you can download sales transactions processed from them. Here’s an article that provides an overview of the integration process: QuickBooks & Square. Better together.
Regarding Stripe, we’re unable to provide a direct connection so you’ll have to use another app. I recommend visiting the App Center to find one that suits your business needs. For Chargify, you can consider contacting their customer care for further assistance.
Please know the data we receive is dependent upon what the third-party application shares with us. QuickBooks Online is like a diary that records what happened to the actual transactions.
For your other concerns, I suggest posting them to the Intuit Developer's Forum. This is the place where customers, engineers, and product developers discuss a variety of development topics and answer integration questions.
I’m adding some links that provide resources to help your business thrive and efficiently handle it.