Hi Kahan!, welcome back!
1. Oath of druids and planeswalkers - I assume if I have an oath in play and my opponent has a planeswalker in play that is not sufficient to trigger oath. Is this correct?
Correct, Planeswalkers and Creatures are different types, and Oath doesn't trigger off Planeswalkers.
2. Memory jar: If I activate memory jar during the current turns EoT step, then my opponent and I get to keep those cards thru that step, into the next turn and swap back to the old hand doesn't trigger until the next turns eot step?
Correct, you can get the cards in the next turn if you activate it during an end step.
3. converted mana cost. On a card like fire/ice I just can't remember: Is the CMC the cost of the spell you cast or the cost of both spells on the card?
While it's on the stack, the CMC is just the half you're casting, but in someone's hand/library/graveyard it has TWO converted mana costs - this can get weird, so if you're wondering about a something specific (Counterbalance, Dark Confidant), you might want to ask about each specific interaction you care about.
4. Platinum angel - I vaguely remember reading about losing the game when this leaves play. Basically Angel is in play, you're library is empty and you can't draw. You are fine. But then your opponent Swords your angel - you lose right there. The article was something about a broken pencil - the angel doesn't stop the pencil from breaking. It just stops you from losing. Once it leaves play the pencil is still broken. In other words once an event happens its condition is always meant. Does this still hold true?
Yes and no, you might be misremembering that article, or it could have been mistaken. Platinum Angel doesn't stop you from going to 0 or less life. If Platinum Angel dies while you're at 0 or less (or if you have 10 or more Poison counters), you'll lose the game as soon as state-based effects are checked (i.e., before you can do anything about it).
That's different than not having a library. You don't lose the game for not having a library, and the game doesn't remember whether or not you tried to draw cards with a Platinum Angel out. If a Platnium Angel saves you from decking, and then it dies, you don't lose the game immediately - you just have an empty library. However, you WILL lose the game the NEXT time you have to draw a card (which is probably at the beginning of your next turn), which means you have only a short window to do anything (like kill your opponent, or get another Platinum Angel in play).