Rounded floppy cables

[orange]

yes, all you need is untwist them

[orange]

I opened and recrimped the connector, its easier and neater. All you need is two cuts, IIRC I included the GND lines on sides when doing the swap (so that the middle is wider).

[orange]

Well I didn't actually recrimp it. I used the same holes, if you understand me. (after opening connector) I had to cut the little plastic tape that holds all wires together so that they are split in three groups. Then just twist the middle group of wires. use colors to see which ones need to be untwisted, I think its pins from 10 to 16 according to this

All odd wires are GND, if you include them in swap, the middle group becomes little larger and more 'stable'..

[orange]

yes, they are (if you look at opened connector); its easy to see which ones need reversing by comparing colours on both ends, in case you got fancy UV cable like me  :-)  
otherwise just use ohmmeter..