I drive Honda Fit Sport 2010 here in Croatia, Europe. Need to change tires, which are all season 185/55 R16 H83. For some raeson it is impossible to find this size. Instead I was offered all season 185/55 R15. Would this difference in the R size be acceptable?
R15 (15" diameter) Tyres won't fit on R16 (16" diameter) wheels, so to fit those you would need different wheels - and the smaller wheels may not fit over the brakes on your car.
A quick search shows that many of the major brands do tyres in 185/55R16, so you should be able to find some - if your local supplier cannot get them, you might be able to order them online and have them delivered either to you, or directly to the fitters. I believe that at least one of the major UK suppliers often ships tyres from Germany, so they may well ship from there to Croatia if you don't have a more local supplier - even with shipping costs it should still be cheaper than buying new wheels!
NO, 15" tyres will not fit on a 16" rim.
Suggest you go to a different shop...
Changing from 185/55R16 to 185/55R15 would make your speedometer read incorrectly by 4.2%.