My answers would be no/yes/yes
The rules for selecting the weapons in the armoury say that when you pick one weapon, you use the first point cost in the listing, and when you pick two weapons you use the second point cost in the list. This means that it would be impossible to select more than one single, standard weapon type because as soon as you select the second, you will have two weapons and be forced to use the second point cost.
We are additionally told that two weapons of the same type count as a twin linked weapon and take up two selections.
The thing to remember is that the passage of text is not optional, it is factual. It does not say if you pick two weapons you can choose to use the second point cost... it really is a simple matter of counting to 1 or counting to 2. If you count to 1 use the first points and if you count to 2 use the second points.
This should also help you answer the second part of your question about the commander.
If the commander gets 2 plasma rifles then we know (using the above) that he uses the second point cost because he must. He now has what is described as a twin linked plasma rifle.
He can pick more weapons, so selects a plasma rifle. This is standard because he only has one plasma rifle (and one twin linked rifle). This means that if he picks another plasma rifle he will have counted to 2 again and so must use the second points cost and create a twin linked plasma rifle.
This mean he ends up with 2x twin linked weapons of the same type.
This train of thinking also answers whether or not you could take a twin linked and a single weapon of the same type.