To get more modern, many people think you don't have a right to healthcare. It is a privilege of the monied classes. Others strongly disagree. We may get near unanimity about slavery -though apparently some xians think it wasn't that bad since it's god-approved in EX21-, but many other topics we would get wild disagreement. So, in the end, government grants (or not) those rights. They can come from nowhere else, and are really just an agreement within society (democracy) or the whim of a single leader (dictator).

Again, that's one way to define rights. Rights are whatever your specific legal system says are your rights. It's not the only definition. I'm not even sure it's the most widely-held definition.

I think most societies and cultures believe that there exists some bundle of fundamental rights (whether characterized as "natural" or "fundamental" or "granted by a Creator") that every human is entitled to even if they live in a society that doesn't recognize them. By not granting them their human rights, their society is denying them their human rights. The person has a legitimate claim that the government is doing something intolerably wrong by failing to respect their rights, even though that claim wouldn't be recognized or honored by the government itself.

This can lead to some weird phrasing. "People in the Dictatorship of Albabia don't have the right to worship freely, so Albabia is committing human rights violations" - a sentence which simultaneously denies a right exists and that it is being violated. This is almost always limited to rights that are considered "Universal" - speech, religious practice, freedom from slavery, etc.

There are plenty of rights that aren't universal. They are contingent on a particular political or legal system. Here in Florida, I have the state constitutional right that my primary residence (my homestead) cannot be subjected to a forced sale for reasons other than taxes or obligations incurred in financing the purchase or development of that property. That's a very specific right that everyone would agree is only a product of Florida's policy preference - not an inherent Universal Human Right. It's just a choice that we Floridians made back in the day in balancing the competing interests of creditors and people's desire for their home to be protected from same.

Yes, while avoiding "god-given" wording.

I mean, not really. The actual language was "[all men] are endowed, by their Creator, with certain unalienable rights...." There's not much difference between "god-given" and "Creator-endowed" - the phrases are synonymous, and both involve the same appeal to the divine as the source of rights that exist independent of whether a human sovereign chooses to recognize them.