No it doesn't tip over on my lap. I think it is balanced based on the angle of the iPad and the placement of the magnetic strip. if you tip it too far forward the iPad will tip towards you. That has only happened when I'm using my lap tray with an added pillow tilting it forward while laying down in bed.
No, it is very stable both in landscape and portrait. In landscape the iPad magnetically attaches to the keyboard so you can pick both up as a unit. In portrait there is no mechanical connection, but the iPad is quite secure working at a desk or conference table.
The top definately makes the ipad heavier but for me it is totally worth it. It doesnt tip over easily when you use the correct side (i.e. magnetic side with the keyboard) but you have to be careful not to use the other side cuz it does tip over then.