Can you set a specific WiFi channel with an iOS/iPhone personal hotspot? Anytime when I using my iPhone as personal WiFi HotSpot (sharing 3G internet via WiFi) the iPhone selects channel #1 for this.

Is possible to use another channel number because the channel 1 is already used by another cable modem / WiFi router and turning on (and using) the hotspot on the iPhone causes noticeable degradation of the speed on the cable-WiFi router.

So the question: Is possible somewhat enforce another WiFi channel number for the hotspot on the iPhone? (e.g. 11 or soo)
No - the OS picks channels algorithmically so you get what iOS chooses each time you enable personal hot spot.  I've seen personal hotspot pick channels 1, 6 and 11 on iOS 7 when in moderately busy wireless environments like this one with 26 advertising base stations (and a few hidden ones as well).