In order...
-Last 16 of the UCL should still happen since Basel and Ludogorets are muppets, but their chances at Top 4 are starting to narrow a bit. They can easily still do it, but outside of Chelsea and, to some degree, Citeh, none of their competitors are really hitting their stride. Aston Villa and Southampton aren't likely to stay where they are, so it comes down to how Liverpool do in relation to Everton, Tottenham, United, and Arsenal, since three of those 5 aren't making UCL next year.
-Maybe. SF121 hit it on the head somewhere in here, they injected a whole lot of new players into the team. Part of what made last year's team great was, as a whole, getting established in Rodgers' system. To some degree, that odometer reset this summer. It may come off, it may not, but there is a need for some patience, which leads to...
-No. Unless they're in the relegation zone come February, Rodgers is fine for at least this season. The bigger question might be the Gerrard question, but that'll come soon enough, I suspect.