OK, tyres. Wheel sizes are invariably quoted in inches, so your 16.5cm is 6 1/2 inches, making your rims 13 x 6.5.
If we now go to
http://www.tyresizecalculator.com/tyre-wheel-calculators/tyre-size-for-rim-size-width-calculatorand feed in this size, we get a range of tyres you *could* in theory fit to this rim:
Tyre widths you can fit
to the rim width: 6.5"
Minimum
tyre width 185
Ideal
tyre width 195,
205
Maximum
tyre width 215
Tyres with
minimum tyre width
for wheel: 6.5x13
185/55R13
185/60R13
185/65R13
185/70R13
185/80R13
Tyres with
ideal tyre width
for wheel: 6.5x13
195/45R13
195/55R13
195/60R13
195/70R13
205/50R13
205/60R13
Tyres with
maximum tyre width
for wheel: 6.5x13
215/50R13
Now you need to see which of those possible tyre sizes is compatible with your original tyre size.
Information on OE Fiat tyres was always a bit hazy in my view. The standard usually quoted was "135 x 12" but this didn't tell you very much as the height of the sidewall is missing. However, I am going to assume that Axel Gerstl know what they're talking about and say that the "usual" standard 12" tyre sizes for Fiat are 135/80 x 12; 145/70 x 12 and 165/60 x 12. Of these, the 135/80 x 12 seems to be the most original "original" so we'll use that.
So now we go to the tyre comparison calculator
http://www.willtheyfit.com/and feed in the original tyre size and the proposed new tyre size. Now the first calculator showed several different options, and you need to look at each one in turn. For convenience, I'm going to take the mid-range of the "ideal" recommendations, 195/60 x 13. I will also use 4" as the original wheel width and 6.5" as the proposed width.
If we do that, we get this (obviously it's best if you do this yourself and see the diagrams on that web site):
Compared to your existing wheel, this new wheel will have an inner rim which is 11.8mm closer to the suspension strut. The outer rim will poke out 51.8mm more than before.
and
Diameter 520.8mm 564.2mm
Circumference 1636.1mm 1772.5mm
Poke 10.8mm 62.6mm
Inset 90.8mm 102.6mm
Speedo error 0% -7.69%
Reading at 30mph 30mph 27.69mph
Reading at 60mph 60mph 55.38mph
Ride height gain 0mm 21.7mm
Arch gap loss 0mm 21.7mm
among other helpful information. In the table above, the first column is the existing wheel, the second column is the proposed wheel.
As you can see, using this proposed wheel/tyre combination gives all sorts of headaches as regards the speedometer reading (now illegal) and clearance of the wheel arches and suspension parts.
You need to do this exercise for all of the possible tyre sizes that could be used on your new rims until you find a combination that is acceptable to you, taking into account any spacers you might be prepared to use and any bodywork mods you might be prepared to undertake.
I've used here two particular sizing calculators that I happen to like and am familiar with, but there are lots of others of a similar nature on the web, if you want to hunt around.
I hope you can see now why earlier in this thread we were asking to know the width of your new wheels. If as you said at the start a 175 wide (that is, 175 MILLIMETRES) tyre rubs the bodywork, then a wider tyre will be even more of a problem.
Just a note on dimensions - I said earlier that wheels sizes are quoted in INCHES. That is, radius and width are. The OFFSET of a wheel (or "ET" from the German) is in millimetres. For TYRES, it's even worse: the width of the tyre (eg "135") is in millimetres, the radius (eg "12") is in inches, and the "80" figure is a RATIO - it means (in this case) that the height of the sidewall is 80% of the width - so in this case 80% of 135mm is 108mm.
A 6 1/2 inch rim is pretty wide for a relatively small diameter wheel (having said that, I've got that for my CC Zero, but being a kit car the wheel arch/bodywork limitations are radically different) and is more usually associated with 14" and 15" wheels unless you go to flared arches.
To avoid bodywork problems you will need to run a very narrow tyre, but on a very wide rim you will be at the limit of what is safe to use on that rim. You'll notice that for your new wheels, the narrowest "safe" tyre is 185mm. That's 10mm wider than a size you already know rubs on the body. So, it seems to me you are faced with either getting rid of the new wheels and buying something narrower (5 inches would be the obvious choice, I don't know if 4.5" are available) or making some fairly major changes to bodywork and/or suspension.
You can see now why I say to get the tyres sorted out before you worry about which wheel nuts to buy.
Good luck in finding a way forward, and sorry if my conclusion is not what you were hoping to hear.