If you need to submit a claim in China, then you'll need to get a fapiao - taxis always provide it, restaurants should but may not always do it on the spot.

But if you are submitting your claims elsewhere (with no need for the final receipt to be acknowledged by Chinese authorities or entity), then the commonly issused receipt - 'shouju' 收据 or 'qingdan' 清单 suffices, and you can just ask for that. I've yet to come across a commonly accepted term for it in China, where every waitstaff immediately understands what you mean, so you may want to keep a sample (say from a previous purchase or from the 7-11) as an example to show.

Fapiao 发票 is an official government tax invoice so requires an extra step (and tax implications) hence the run-around in some places.

Credit card acceptance is variable - fancier ones definitely do, but fast food and smaller establishments will only accept the Chinese Unionpay, no visa/mastercard/amex.