Dominant hand and not dominant hand do not matter in Kenjutsu. Most people are right handed so the sword is ALWAYS drawn with the right hand if you are a lefty or not and if your sword is sheathed or not. Since most people are right handed and therefore will draw their sword with their right hand it is in your own best interest to do so as well. You can draw and cut in one motion. If you draw and cut in one motion with your left you will cut the left arm of your opponent facing you and guess what he has in his right hand waiting for you which he undoubtedly will use to kill you even more so now because you cut off his left arm. If you draw and cut in one motion with your right hand you will get your opponents right arm and a well aimed cut will render the arm useless to even lift for a cut.
How? If you are in that desperate of a situation to draw a sword when unprepared to do so it's any which way you can get it out of your sheath without cutting off your own fingers in the process. Don't laugh, many people cut themselves unsheathing a katana.
Other than that yes, drawing the sword without it being attached to the obi was definitely done when circumstances dictated so but was not common. After all not too many samurai went to bed with their katana attached to their sleepwear and on occasion did have to defend in the middle of the night. No time to tie a katana to your belt then. I know silly example but you get the idea that the sword was not tied to the obi of a samurai 24/7 but was always within his reach.
And yes the sheath was also used as a weapon to strike and if you know where, you can deal a lethal blow even with just the sheath or use it as a distraction for a cut.
The same way you'd draw it from a belt. Hold it at your hip with your weak hand and draw with your dominant hand.
There were (probably still are) a few schools that taught the use of the scabbard as a secondary weapon. Scabbards might not be solid but getting hit by one can often hurt enough to create an opening to strike through, they can also be used to lock up a sword long enough to swing a killing stroke.
While it is not at all common it isn't unheard of either. I know one or two moves in Kenjutsu that are usually for two swords but can easily be adapted to use the sheath if you don't have a second sword.
When a samurai got into a duel with every intention of fighting to the death (referring to his death), especially when dealing with multiple opponents, they would discard the sheath or scabbard of their katana.
yes
You see in movies and anime people holding a sheathed katana in their hand and unsheathing it, do people actually hold unsheathed katana and not attach them to their side or similar? If so how do you draw you blade effectively?