I work at Stripe on Developer Relations. On the client side, using a library is important to ensure that sensitive card data never hits your servers so you don't have to worry about PCI compliance. On your question about the API, since you're using Firebase, have you looked at Google Cloud Functions? The Firebase team put together some examples [0] to accept payments with Stripe easily from your apps by simply calling functions. Please let me know if that's close or different to what you had in mind.
[0] https://github.com/firebase/functions-samples/tree/master/st...