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With proper care, it should not dry up. They will, typically, produce a second round of flowers, and sometimes even more. You my cut only the dead or drying parts. It can be difficult to get them to reflower without proper knowledge on how to do this. It isn't mentioned in the article, but it is also important to note that many orchids require a change in duration of light to force flower. A pitch black period of over 12 hours per day will help initiate flowering. While Longer light hours will increase leaf growth. These links will give you some more information.

https://www.gardeningknowhow.com/ornamental/flowers/orchids/indoor-orchid-care.htm
https://www.gardeningknowhow.com/ornamental/flowers/orchids/make-orchid-bloom.htm

Just be sure that the orchid does not get direct light all day. This will worsen your issue. These are very cold sensitive. Now, unfortunately... There is a list of requirements that must be met in order to get this to bloom again. Orchids are photoperiodic. This means that they will not flower until the hours of pitch black darkness exceeds the amount of daylight that it receives. You must first give it about 18 hours of bright, but indirect, light per day for a couple of months so that it can recover. Do not cut the flowering stalks as they can rebloom from these. Now after the couple of months of long day length, you will want to make sure it get less than 12 hours of light per day, and more than 12 hours of pitch black per day. This simulates a "winter" without the cold. After you meet these requirement, and a few more, then it will flower again.

Here is an article that explains everything but the Change of the light cycle. I have given you that explanation above: https://www.gardeningknowhow.com/ornamental/flowers/orchids/make-orchid-bloom.htm

Since flowering takes up a good bit of resources, I would say to wait until after the blooms fade to remove this.

This article will give you more information on the subject: https://www.gardeningknowhow.com/ornamental/flowers/orchids/orchid-keiki-care.htm

Yes, orchids need special, very fast-draining potting mix. It is sold as Orchid mix and is widely available in the US at garden centers and home improvement centers. Hardware stores may also stock it if they have a decent-sized garden section. Orchid mix has lots of bark in it so water drains. Regular potting mix is too rich, too wet for orchids. Here is an article describing the repotting procedure: https://www.gardeningknowhow.com/ornamental/flowers/orchids/repotting-orchid-plants.htm

If the branch has broken off then there will be no need to cut, as it has already done it for you. Just let it recover, and put it through the standard photoperiods for vegetative growth and then flowering. The stalk will produce from whatever is left of it. Pruning any more will stop flowering for another year.

Orchids cannot, under any circumstances, tolerate direct sunlight. These grow in the canopy of trees naturally, and therefore, only receive dappled light. This is the issue here. They are burning because of too much light.

Here is an article for more information on their care: https://www.gardeningknowhow.com/ornamental/flowers/orchids/indoor-orchid-care.htm