If the flat was due to broken glasses/metal wire etc., that means the tire has been damaged, so carrying a pump is not enough--you'll need to fix the tire (patch etc.), quite a job to do on the road, isn't it?
I ask again ... have you actually purchased a bicycle and started riding yet? Your questions sound like you've never ridden a bicycle, and never encountered things as common as flats.
No, unless there's a gaping hole in the tire, which does happen but only occasionally, your tire is usually all right if the flat is because of broken glass/metal wires. It's your tube that needs to be replaced or patched. Inside the tire there are tubes. These tubes cost about $2-5 so many of us carry a couple around with us, and maybe a patch kit, depending on how far we ride and what sort of conditions we ride in. When you've practiced changing the tire in the comfort of your own home several times, so that you are familiar with the process, you might be able to get the time of the changing process down to 10 minutes or less. For me, the time consuming part is determining where the teensy little shard of glass is.
If it happens that you've gone over a sharp rock and there is a noticable hole in the tire, you will take your tire boot out of your bag, then boot the tire, change the tube, and be on your way. Booting the tire will take an extra minute ... the time it takes to get the boot out of the bag.
And because I suspect you'll ask, boots can be anything from commercial boots you can buy from Park Tools to paper money to sections of old tubes, or other similar things.