You ask an important question. There is an A T and T language line (I've never used it, since the maj of my patients speak engliah or Spanish and I speak both, (thank goodness) but using an interpreter does not always make people feel like they are in a trusting relationship. If they speak english and the culture is foreign to you, maybe you can ask some simple questions about the culture. I have found that most people do not expect that you will "know" their culture, and showing a genuine interest in it goes a long way- it shows respect etc etc etc. But if there is no english and no translator, it does get difficult. Remember for the pt this is an entirely terrifying experience, I get called all over our hospital when the Spa interpreter is tied up elsewhere. Sometimes just your actions- getting a blanket, repositioning gently etc, can make a big difference.
I also have never seen a nurse/pt relationship get too close. It depends on who you are. It really is a learning process as well, to not take all your pts mentally home with you. Yes, I was very well prepared to develop appropriate pt relationships: it was focused on in every clinical and before we even started clinicals.
Crossing the line is a very individual thing: It depends ont he relationship you had with the pt. I was a Home health CNA and took care of hospice pts. I occasionally attended funerals, as I had been in the home every day for sometimes months. The family seemed to find it supportive, and it did give me some closure. Now, as an ICU nurse, I do not attend funerals (Thats all I would be doing on my days off), but I haev a very different relationship with these patients, I don't often get to know them as closely. I think it is very individual.