Well, it depends on what you mean by 'train'. If you're talking about combat training with specific NPCs, some might stop offering training after the story is over. However, you can still level up your skills through normal gameplay like fighting enemies, using magic, or picking locks. So in a sense, you can still 'train' but not in the traditional way with some NPCs.
There are generally no new training opportunities after you've beaten the story in Skyrim. The game's design is such that once the main narrative arc is over, the focus shifts more towards exploring the remaining content of the game world, like hidden areas, side - quests, and collecting unique items. While you can still improve your skills through normal means like combat and using magic, there are no new training mechanisms introduced at this stage.
Yes, in many games it is possible to max out your companions even after beating the story. This allows you to fully upgrade their abilities, stats, and relationships. It gives you an opportunity to further explore the game world and complete any remaining side quests or activities related to your companions.
Well, it varies. Usually, it's determined by the game's design and rules. Sometimes there might be additional challenges or conditions to meet for maxing companions even after the story is completed.
Sure. Once you've beaten the story in KotOR, there's still a lot to engage with. You can revisit planets, interact with different characters in new ways, and try out different playstyles or builds for your character. For example, you might have focused on a combat - heavy build during the main story, but afterwards you could try a more diplomatic or stealth - based approach and see how that changes your experience of the game world.