What happens if you pucture out on the road? Will a mobile phone be the only practical option?
You carry spares.
The traditional place for the spare tire is under the seat.
The proper glue is not only available in tins, but also in small tubes. Have one of those with you too.
Once punctured, how are they repaired?
The tire casing is sewn closed around the tube.
Pull the tire off the rim. If it is correctly glued to the rim, this is something that will separate men from boys.
Locate the puncture. The classic "put the tube in water and look for bubbles" test will almost always point out whereabouts the puncture is located.
Peel off a part of the cotton band that is glued on top of the seam.
Cut the sewing thread to open up the tire. Just as much as you need to get the damaged part of the tube out of the tire.
Repair tube as usual.
Put tube back into tire.
Sew the tire back around the tube (this is probably the most interesting part, working with a sharp needle in a bicycle tire, all the time trying not to get too close to the tube)
Glue the cotton band back on top of the seam.
Ordinary needles and thread won't do, you'll need beefier stuff like for sewing in leather. I'm using needles and thread I got from a sailmaker.
Can a numpty get one on a rim so that it stays there?
It's not that difficult, really. They can be a really tight fit, though. Be prepared for the taste of blood in your mouth when trying to wrestle a stubborn tubular onto the rim.
How the flinking blip do I pump up the tyre of a carbon disc whell that only has a small cut out of one side of the wheel?!!?
Dunno. Pictures of the wheel/cut out?
When it's 20 below freezing and the snow lays 10 inches deep, bicycle commuting kind of sucks.