1) Not sure about 3rd party videos. I did a few tutorials on PokerStrategy.com that are available for free, although slightly outdated by now:
https://www.pokerstrategy.com/video/39510/
https://www.pokerstrategy.com/video/33261/
Updated tutorials are coming with the next major update.
2) CashEV Raked is, well, raked. You can specify a rake% and $-cap and then enter chip stacks in $ to calculate raked cash game hands. Regular ChipEV does not use any rake.
3) I think many of the push/fold charts are based on the free web calculator, which would be less accurate than the calculations in HRC. Seeing 66 but not 77 is quite normal, 66 has higher equity against tight calling ranges.
4) CALL charts are more dangerous, as it's easy to make -EV plays if your opponents deviate from Nash. PUSH charts are more robust in that sense, at least in early game where ICM considerations are not that significant. That's why CALL charts generally aren't very popular or useful.
5) PokerStars/FTP do not allow any ICM calculators to be open while their pokerclient is running. We try to detect if PS/FTP run and close down HRC to avoid any issues. I'm happy to add detection for additional sites if HRC is not allowed there, but don't take the absence of detection as an indication that HRC is allowed on your poker site. Please check the ToS on Ignition or contact the support to get a definitive answer if the terms are unclear.