binance seems to have BTC-EUR but no BTC-USD. I can see BTC-USDT. Is this the closest one to trading BTC-US dollar?
It makes sense to me that they don't offer a USD trading pair, as binance does not have access to the US banking system, much less so to the or a federal reserve account.
How they are able to represent the euro in the first place within their exchange/framework, i don't know. That would mean they would have an account at a EU bank and subsequently at a NCB within the eurozone, which i highly doubt given they operate with and within "anonymous" accounts. (I highly doubt this would be allowed by the ECB and subsequently their commercial bank), If anyone could shed some more light on this and how this would actually work (I fear I might be wrong here.), I'd be extremely interested.
Before thinking you can use USDT as a safe haven, you should note that more often than not, these "stablecoins" are not backed 1:1, or at least not proven to be, and that while they might be stable as of right now, that that is not a guarantee for the future.
USDT in particular lacks audits. A quick google search on the topic will give you a wide range of articles why they're so controversial.
Anyway, to answer your question, yes, USDT is probably the closest to representing the value of an actual dollar, but, as i said, it is NOT an actual dollar, and you should be really careful using them, or preferably; not use them at all.