Here's my take on these "issues" (nope, they still suck... though some of them could've been made to work):
1. Why Luke doesn't want to kill the Emperor - If he did, he'd slide into the dark side.... not because moral considerations, but because the manipulative bastard has riled him up into a good rage and made him hate his guts... if he lets loose he'd irrevocably fall. (Yes, I know it's idiotic, but this is how the force is portrayed in the overwhelming majority of the franchise). In the end he'd become just another well intentioned extremist. That's why the throne room was a trap, since as far as the Sith were concerned they've already won: If Luke kills the Emperor, then he'd team up with Vader and a new pair of Sith would take over the empire. If Luke kills Vader, he displaces the old apprentice and the Sith live on. Why would he do either of these? Because the dark side is seductive (I know, I know... but this is how the Force is portrayed... yada, yada)... so once he got a taste he might take more compromises.
2. Why the Imperial Navy didn't trash the Rebels even with the Death Star and the Emperor gone:
Imagine the bridge of random Imperial Star Destroyer with a high ranking admiral aboard:
-Admiral the Death Star's gone and the Emperor dead!
-Dead? Then who's in charge now?
-Errr....
-Hmm... hey, since I'm pretty high on the ladder I could be. Open a comm channel to all ships! This is admiral as the admiral of greatest seniority I'm taking charge of the fleet, so...
<another comm cuts in>
-....am assuming direct power for the...
<another>
-....so it's clear I should be the...!
<another>
-No, I'll never stand for it, I have Moff Jiles onboard and as part of the direct leadership appointed by the Emperor, he should...
...get the picture? The moment the Emperor's gone, with no clear successor the whole leadership could break down. Without a charismatic and acknowledged person like Thrawn, Dalla or Tarkin around the infighting could tear the fleet apart...
...and even if it didn't the officers would be very nervous about taking initiative on their own as Imperial doctrine discouraged wildcards and solo action. They don't know who'll be in charge and just in case they would keep as much of their forces in reserve as possible. So they'd retreat.... taking out the rebels would be a lesser problem, right now with the political turmoil ahead they'd focus on preserving their career.... or life in case the takeover gets hot.