I always interpreted the Planeswalker cards as mere beacons beseeching the aid of a friend in the moment of need. No clone shenanigans, no space/time manipulation, just a friendly request for aid and an offer to return the favor in due course.
The planeswalker teaches you a spell to contact him, regardless of his location in the multiverse, at the moment you form an alliance with him. This spell doesn't represent the planeswalker himself, and as such it doesn't need to meet the same color-requirements of the planeswalker (explaining why, for instance,
Nissa Revane 
, though she wields both Green
and Black magic, only costs Green); all the spell does is send out a call for help and a timestamp, telling the planeswalker who is calling and from where. The planeswalker then determines whether it's worth showing up (the game abstracts this to 'always shows up' for simplicity and fun) and which spells to bring.
The reason a planeswalker always brings the same spells when you use the same beacon is likely because of the nature of the relationship. You met the planeswalker under a certain set of circumstances and saw his repertoire at that time. The beacon he gives you at that moment encodes the style of magic he was wielding, because if that's the version of him you know, and you're now sending out a call for his aid, it's likely because you've determined that repertoire of spells is most beneficial in your current situation. He could show up wielding a different set of spells, just like he could just choose to not show up at all, but the game abstracts this as well.
Finally, the reason he doesn't have any memory of loyalty to you. Again, this is an abstraction to make the cards work in the game, but I'll take a crack at the flavor nonetheless.
Every time you summon a planeswalker, you're promising a favor in return. Some planeswalkers may be more friendly to you, but this isn't represented by a memory of loyalty from the last time they were summoned; rather, it is represented by an overall higher starting loyalty. The planeswalker determines the value of a return favor from you, and that is represented by his starting loyalty. He always comes with that estimated value in mind, so his starting loyalty is unchanging. Letting him do simple, fun spells isn't very taxing, so he doesn't count them against your eventual return favor; however, the more powerful magic at his disposal is valuable, and he knows that, if you ask him to use it, he can then ask you for a greater favor in return, and thus doesn't need to stick around for as long to get a valuable use of you in the future.
Edit: Additionally, the reason for the 'lengedary rule':
When a planeswalker is fighting on your side, and your opponent calls in a favor as well, he cannot fight for both of you. As such, he interprets the opponent's favor as a request for a return to neutrality, and he 'walks away. This is especially beneficial, as now the both of you owe him a favor, and he doesn't have to do anything for either of you to gain it.
