My question is
1) Does Audyssey checks impedance of speakers while doing room correction
No
2) Do I need to change impedance before doing Audyssey
No, you can change it any time before or after. Please note that if you change it to 4 ohm, the SR6013 will limit the output. If you don't listen very loud and sit not too far away from the speakers, you don't have to set it to 4 ohms. We can say this in a more definitive way if you provide your room dimensions and seating distance from the speakers.
3) since I have done already setup do indeed to change impedance to 4 ohm or I need to change impedance and re run Audyssey
No need to re run Audyssey.
4) bass management- lfe alone or lfe plus main
It is up to you, if you set the main speakers to large, lfe+main will allow the subwoofer to play the lfe channel contents and will also play/duplicate the low frequency signal send to the main speakers. If you set it to lfe, the subwoofer will only play the lfe contents and the low frequency signal in the main speaker channels below the crossover point. So if the main speakers are set to "small", lfe or lfe+main really makes no difference.
5) cross over frequency how much to keep
Audyssey got 120 can I keep same or change it to 80
Again, it is up to you, you can leave it at 120 Hz, or try 110, 100, 90, and 80 Hz and then stick with the one you think sounds best to you in you main listening position.
