How many Planeswalkers appear in Core Set Displays
OK. There seems to be quit a few misunderstanding here, but I think I managed to identify a core one.
Magic the Gatherging can be played in several ways, the 2 most importat ones being draft and constructed.
There are also quite a few different products out there. Some suite one play style. Other suit the other. Some, especially in case of draft play, are absolutely the wrong way to do things.
But lets work on the assumption that you want to play draft. These are usually organized by game stores or by groups or friends. Either way, what you need is 3 draft boosters per player. (Usually 6-8 players in total.) Please note that non-draft booster products also exist, namely the new set boosters. These are not designed for draft play. 2 player draft variants also exist, but I will not get into those right now.
As for what set to get, most products are desiged to be drafted set by set, meaning (at least for all sets in stores right now) all the boosters for all the players would be from the same set. Doesn't matter if it is an &quot;expansion set&quot; or a Core Set. In modern MtG Core Set aren't that different from any other set. They just tend to have a bit more simple design in the cards they offer, to offer a better starting point for newer players.
What about Planeswalker Decks? Those are mostly intended as a starting point for constructed play, where you build a 60 (or 100 for Commander) card deck from any cards from any sets that are considered legal for the format you wish to play. Most beginner friendly constructed format (outside Commander, that's a bit of an exception) is Standard.
Trying to draft these decks would be... odd. Not impossible, but they really aren't meant for this.
Given all this, your 3rd question kind of becomes irrelevant, but let me just state that no deck needs planeswalkers. The are pretty powerful cards and some decks can make great use of them, but others will work just fine without them.