Have you tried adjusting the nozzles? I know the older type do adjust not sure about the new ones. If its older ones you can adjust them inward a bit more on the glass. Or up/down so you don't get as much back splash.
Old type: Two seperate streams - just need a toothpick or a small pen cap to adjust them, the actual nozzle does have some play in it.
New Type: Fan spray/mist - I have no idea if these are adjustable, never tried I don't really use the washers on my car that has these ones.
Right now add distilled water to what you have in there til you clear the blue stuff. Its most likely going to stay warm enough so it won't freeze.
I did a search through NAPA and Kragen/Schucks and came up empty for a clear wiper fluid. Pretty sure it does exist though, it has too. There are car freaks that won't have a color in their wiper fluid. But why not try something like this til we find it?
Mequiars NXT glass cleaner is clear, you could also buy a bottle of that dilute it down with distilled water so you have volume and use that..
In the winter though if you are in an area that does freeze try swapping over to the pink stuff and cut it down with distilled water, should keep it from freezing and hopefully won't stain as bad. Or mequiars does have a hotline to call and find out if they know if it freezes or not.
Chrome bezel easy
Damp microfiber cloth followed by a dry one so you don't get wipe marks on it. A gentle splash of a quicky detailer if its really grubby then just a dry microfiber til its pretty then the damp/dry from then on.