There are some explanations for the other ones:
1. Kaiba cheated to summon Blue Eyes by stealing Sugoroku's card and using it against his grandson in a Shadow Game, in which cheating (and therefore lowering one's pride and spirit enough to break the rules) is punishable by defeat and a Penalty Game. The worse offender would be when the Ventriloquist of Death in the DK arc summoned a Blue-Eyes in a holographic Battle Box and it killed itself for no better reason than kaiba's love for his card... even though he stole them from other card collectors in this continuity. The anime made it better by having Kaiba directly hack into Pegasus' system. Still cheating, but whatever.
2. This is really stupid but Yugi's friends already helped Yugi/Atem win against Yami Bakura in the Monster World game, and Shadow Games quite often employ the "screw the rules" mentality anyway, especially with Kaiba asspulling an Obelisk draw out of nowhere despite not even having the card in his deck in DSoD.
3. Explained by Kaiba's past life having owned the Rod, plus it's through this that Kaiba was able to read and decipher the second and third abilities of Ra.
4. In the manga, the Memory World is explicitly stated to just be a recreation of Ancient Egypt on a sand diorama that is animated through the sealed memories of Atem and Zorc/Akhenaden that were contained in the Millennium Puzzle. It's the anime that tried unnecessarily to up the stakes by making it some space and time magic doohickey where they were playing on a floating game board in some shadow space that was literally creating a recreation of the past and causing disruptions in space-time and destroying the world for real. Manga-wise Bakura just fought to resurrect the Great Priest of Darkness Akhenaden (Zorc Necrophades) and to learn Atem's true name to unleash the main body of Zorc that was sealed in the Millennium Items and the Meikai.
Granted, Takahashi seemingly intended for it to be a literal travel to the past in the early stages and changed it to a simulation of the world of ancient Egypt so that Atem's friends could participate, but he clearly explained that Atem's memories were used to create the diorama in the present rather than them literally traveling to the past.