Problem #2: if the inactive tab is paused and the game is unable to run normally (it's forced to pause or to skip steps) it may result in a corrupt result which - in case of a duel with cash at stake - might seriously affect the contest holder's reputation
What do you mean by "corrupt result"? It's a useful feature to pause games in inactive tabs to help save CPU and battery on laptops and mobile devices. The game properly resumes from its previous state without any problems, unless there are bugs I'm unaware of. If you want to run a cash competition and you really think that's a deal breaker, I'm happy to say Construct 2 is not the best tool for that job.
If you can reproduce the IE problem, let me know.
Large skill gaming websites, such as king.com, are still using Flash for their new games, and they probably do it for a good reason.
Maybe it's because they're too slow to get with the times! :)