1. With Lua script & a hookFunction to update the displayed text position & a couple of eventHandlers to detect when displayed text starts & ends. As for the videos... I'm not sure. The recent feature of being able to attach videos to scene objects & play them directly in scenes is new & somewhat still raw as there doesn't seem to be any options to currently scale them to specific sizes or position them where you want them into a scene.
Anyway, check example 1 here
for an example on how to force the text position.
As for textStarted & textStopped event handlers, they work in a similar way to the hookFunction, but they are only triggered once per new text start/end whereas the hook continuously loops to keep the text in the same place.
-- do something
-- do something
2. I'm not going to tell you how to create a chess mini-game as it would take forever & I doubt I could explain it off the top of my head. All I'm going to say is create a menu type scene instead of a scene type scene. Technically you can create a regular scene too, it doesn't matter, but if you don't need to let the player access the inventory & don't need the way system & so on then what's the point? As for a first person puzzle... check out this
sliding puzzle example I created & shared on the wiki. It was scripted with Lua & uses tables to form a grid, which is something you would probably have to do for a chess based mini-game, though it would probably be possible to create without scripting if you are willing to create 100's of values, conditions & if queries in the editor.