A common (but probably not entirely grammatical) way to ask this is: How many of you are there?

I think "How many in your party?" or "How many are in your group?" would be the most appropriate. Those expressions also sound more positive and friendly from a customer service perspective. "How many?" is terse and sounds a bit rude and unwelcoming. From a customer service perspective, you may appear to be uninterested or like you don't care about the customers or your job.

I think it would depend on the restaurant and just your personal preference. For example, a more high-end/expensive restaurant would probably ask something similar to what you said, "How many are in your party". In a more casual setting, for example, if you're eating outside or somewhere that isn't as expensive, someone would probably just ask "How many chairs do you need?" or "How many". Honestly, there's not really a perfect answer, as long as you're not rude when asking however you want to ask isn't a big deal.