Ordering drinks

I searched online, and it said that warm water is onsui, but does onsui refer to warm water for drinking or just water for public baths and showers and such? Futhermore, for hot and warm tea do we just add atsui and atatakai in front of ocha?

Lastly, how do you ask for a refill such as, " do you think you can help me refill hot/warm tea/water?"

Yoroshiku Onegaishi

When we order warm drinking water, we usually ask for "o-yu".

For example, if you're sitting at a restaurant you can say
"o-yu kudasai. (warm water please)"
and you'll get a glass of warm water.

If you're asking a hotel staff out of the blue, you may want to say "o-yu o Ippai kudasai." (with the accent on the capital I)
so that you can get one glass of warm drinking water instead of a bucket full of hot bathing water.

It's not that it's incorrect to call warm drinking water "onsui", but it's not common.

Futhermore, for hot and warm tea do we just add atsui and atatakai in front of ocha?

If you want it warm as opposed to cold, you should add "atatakai" in front of the drink name.

Meanwhile, "atsui (drink name)" means that it's sort of too hot. So if you ask for "atsui ocha", the waiter will think that you prefer particularly hot tea that is so hot it's almost hard to drink.

Lastly, how do you ask for a refill such as, " do you think you can help me refill hot/warm tea/water?"

The younger generation often use the word "refill" (pronounced more like ri-fi-ru), but it's best to show the bottle and say something like,
"kore ni o-yu o irete kudasai." (please pour warm water in this.)
and point at the level as you say,
"kore kurai" (about this much).

Or if you are simply asking for an additional serving of whatever you were just drinking now, you can ask for
"okawari" (additional serving)
as you point at your glass.
Or you can say
"o-cha no okawari o kudasai." (An additional serving of tea please)
to be more specific.

Hope it helps.

They sometimes charge you for refill, so I would say "Okawari wa dekimasuka?" that contains the meaning of "Could I get a refill for free ?"