do I make something wrong?
No you dont make anything wrong you expect something that's not true about maya in general even with polygons. Your passing judgment based on very low quality previews. Missing the core idea behind DCC 3d apps in general.
#1
The surface si closed in on itself so what you see is the close part turning back on its own surface causing artifacts. Happens even with polygons if you decide to do this. You have 2 surfaces on top of each other by mistake.
You dont look ate the view ports alone in maya you look at the data the sitory and so on, so 1/8 of everything you do because you MIND tells you its right, the viewports dont help you on most of the things you'll encounter. Knowing the data does, thsi si why 3d is significantly harder than 2d. And no it cant be helped much.
#2
Ok your confusing 2 things here, whet you see in your view port IS NOT WHAT YOU GET, its a approximation see the thing is your 3d hardware can just draw triangles,its accelerated that way a straight edge can never become curved, the mathematically accurate nurbs models is tessellated built out of triangles.
The more triangles are put in place the more accurately it will match your surface, but the slower it gets. Now the software renderrers have a trick up their sleeve*, they don't need to accelerate all possible view directions so they can actually make enough triangles. Same applies to illustrator it also doesn't need to worry about other directions. Take this example picture:

Picture 1: see how the render view on the left is perfect in shape, it also has beautiful AA and color correction all of which the view port that's a preview on the right does NOT have.
So you should not give verdict on what something is based on your previews. Ok so tessellation can be done better, CAE** apps certainly do, however it doesn't really matter for how 3d graphics artist work. You can adjust the tessellation accuracy with the Display -> Nurbs -> Custom Smoothness option. It just gets slower. Its atradefo the more accurate you want to be the slower it gets to use. Offcourse since your not really interested in the 3d vies but thE end results.***
So you don't trust your eyes with maya and nurbs you trust your MATH.
#3
that's what you told it to do. If you wanted the hole you'd also had selected the hole. The computer isn't intelligent it just does explicitly what you tell it to do even if you dont realize it yourself. Maya isn't working on solids just the data you push in and each surface is unaware of all else (save construction history points)
- ok the gfx card could do this, but i don't think you'd appreciate 1 frame per 2 seconds update times even with simple geometry. Theres lots of other things your view ports don't do either which is why you renders stuff (we wouldn't do hour long renders if we could have then 24 fps is our view ports)
**CAE is what CAD applications have become, even if you call them CAD's they are still all CAE apps today.
*** Well thsi is number one failing of many users, they get hooked up on the way and never get to the end result. You ought to keep an eye on your renders at stage one, its important you can aert so many problems when you do.
Quite obviously you wouldn't use nurbs for game models much, unless your game a engine supported b-rep which is HIGHLY doubt. Or you duse the nurbs to do patch matching tessellation yourself, but then again id doubt you'd use planar for anything.