Hi, on the first part of your question - Yes it would be fine to ask; "Hi, I need to repair my car. It has a problem with the XXX. I would like to know how much it will cost./I would like to get a quote. Thank you." It's also very common to ask "Could I get an estimate on how much it would cost to repair it." On the second question - If the quote is more than you expect, depending on the store and country you are in, you could either haggle about the price, or politely say, "thank you for the quote, I'll let you know when, or if, I'm ready to get the work done."

I would open with the word "quote" as early as possible so that the mechanic doesn't get all excited when you describe an expensive problem and then close with "oh, but I just want a quote from you". :D And asking for a quote is the same ask asking how much it'll cost; there's no need to say both those things. I would say "Hi, could you give me a quote for fixing XXX on my car, please? Thank you! :)" And, I would always respond when people help me out (and sending you a quote after you've asked for one is helping you out) just because it's the respectful thing to do, no matter what language you or they speak. The minimum you need to say is just "Thanks!".