How normal is it that a person would ask something this politely in Israel? I thought people always asked questions head-on...
As a theoretical question it would be quite common, for an actual suggestion - not so much..
Yes, it literally means "you were".
However if you put it in the beginning of a question, it's just a very polite way of asking a question (very similar to :would you like").
Did you want to come with me - "רציתן לבוא איתי", I think I see where the confusion is coming from, but we don't have anything in Hebrew which is similar to the perfect/progressive tense in English (just simple).
I is good that they accept all good options. That said: As a normal polite resquest, I guess, "would you like to..." is much better and more common than "would you want to." and they mean exactly the same in this context.
I can try to explain it clearly but it is going to be long so brace yourself ;) In Hebrew when you want to ask someone about something THEORETICALLY you would ask "האם היית/הייתם/הייתן + פועל בהווה" or the same without the האם (it is optional) For example : If I have asked you out , would you agree? אם הייתי מציע לך לצאת איתי, היית מסכימה? If I were rich, would you love me? אילו הייתי עשירה, היית אוהב אותי?
Now, your sentence (did you want to come with me) is not theoretical (english speaking) but a simple past tense sentence , and so it would be translated as רציתן לבוא איתי ? Here are the forms of the verb לרצות present and past l אני רוצה (rotze male or rotza female) / אני רציתי (ratziti) אתה רוצה (rotze) / אתה רצית (ratzita) את רוצה (rotza) / את רצית (ratzit) הוא רוצה (rotze) / הוא רצה (ratza) היא רוצה (rotza) / היא רצתה (ratzta) אנחנו רוצים (rotzim) או אנחנו רוצות (rotzot) / אנחנו רצינו (ratzinu) אתם רוצים (rotzim) / אתם רציתם (ratzitem) אתן רוצות (rotzot) / אתן רציתן (ratziten) הם רוצים (rotzim) / הם רצו (ratzu) הן רוצות (rotzot) / הן רצו (ratzu)
I hope it is all clear and that it helps :)
So how would one translate 'would you have wanted to come with me?' , which is in the past and meaning that there is no option anymore to come with me?
I'm no grammar expert, but you can't give a direct translation to this sentence which indicates both the past tense aspect and the conditionality. You could however, use other words to indicate that this option is no longer available. I would translate it as so: היית רוצה לבוא איתי, לו יכולת? (Haít rotzá lavó ití, lu yachólt?) Which basically means "Would you want to come with me, if you could?" but in the past.