"Um, excuse me, where is the restroom?"
is 「トイレ」 really casual terminology? i seem to remember reading that it literally means "toilet", as in the toilet bowl, and that 「おてあらい」was the more polite word to use when referring to the restroom - esp when speaking with strangers, elders, superiors, etc.
the other sentences are
1) "toire wa doko ni arimasuka?"「トイレはどこにありますか？」 and 2) "toire wa doko ni aru?「トイレはどこにある？」
the (1) means "is there a toilet"? the (2) means the same, but, if i'm right, it's in a less formal form, and lacks the "ka" in the end that is the question marker.
i'm thinking it may be because it sounds like you're apologizing, and have casual grammar mixed with polite or more formal style words?
*「ええと」 = umm / well / let's see...
*「ごめんなさい」 = i'm sorry (slightly polite form, apologizing for something you shouldn't be doing or have done)
*「トイレはどこにある？」= where's the toilet (casual form)
But what if im apologizing for making them waste their time on me.
Or what if someone wants to confirm if i know where the bathroom is, but i know that they think i know, but in reality i dont. In escence i would be apologizing for the mindgames, like i should be doing now.
it's technically correct, but i remember reading somewhere that in practice japanese people always write 「すみません」 only in hiragana because the kanji stem 「済む」 implies something totally different and just confuses things.
another nitpicky thing that duo might be getting caught up on is the maru (period) at the end of your sentence instead of a mimidare (question mark).