-Depends on the item. The Eye of Charon was indestructible without the Tear of Charon. Otherwise why does it being magic necessarily mean it's indestructible?
-Not true, it'd have to be a magic weapon meant for that purpose otherwise it's just a magic weapon. If it's enchantment still applied then great! If not...well..it's still a good weapon.
-Choking mists, animated statues, guardian demons, walls of force. All of there were in just one fortress. Again it depends on the magi's fortress. I haven't seen one as un-breakable as Orthanc but that's not saying much. This doesn't include actual guards or mechanical traps which you see every now and then.
-Conan is actually wearing clothes more then half the time. And armor too. Comics portray him otherwise.
-This falls back to specific items and the 'why does it become harder to destroy just because it's magic?' again. Conan-verse takes a more realistic view on magic items. Just because it's magic clothes doesn't mean it can't rip or tear unless specifically enchanted that way. Same with weapons and whatnot.
-See above because it still sort of applies.
-That's still workable, surprisingly enough, for Conan. And please note before you charge this statement I am not saying it'd be EASY. It'd still probably be very very hard but it's doable.
-Stealth elven cloaks are for those who can't hide on their own.
LOTR universe has more prevalent magic and magic items. I don't think anyone will argue that but the point is Conan does what he does without magic half the time. That's the basis of Heroic fantasy. It's all coming from the hero. If Frodo had managed to get to Mt. Doom on his own, resist the ring and toss it in purely by his own efforts without magical doodads then that'd be more Heroic Fantasy then High Fantasy. In every story he's abandoned magical things because they make him uncomfortable, that's why he finds the things that would allow him to do amazing things but afterwards gets rid of them because they aren't what makes him a hero. Conan, tossed into LOTR verse would struggle for a couple months to adjust (That's on the long side) but after that he'd be right as rain because he learns and adapts.