They are air roots. Which is completely normal for this type of orchid. So absolutely nothing to worry about. Therefore be happy, as this means your plant is healthy and in the mood to grow - Don't worry as it's not an alien invasion.
I think you shouldn't, as it's something the plant put our naturally - I haven't kept orchids, so I really can't say for sure. But I think they are air breathing in a way, (taking nitrogen from the air). Or even if they are just for the plant to attach itself to another tree's branch, (meaning that it's strictly for structural support only) - They still have a purpose of some type. Again, I haven't kept orchids. But it could be that now you have the option to divide the plant and have 2. So maybe you'd like to propagate it? Not sure though, will have to look it up. But generally, just to be on the safe side, I wouldn't cut anything until I learn more.
Most orchids are tropical plants which live as epiphytes or "air plants"hanging on to trees for support with roots. Some orchids are lithophytes or "rock plants" growing on or among rocks. The remaining orchids are terrestrials which grow in the loamy detritus of the jungle floor. See you tube videos on growing orchids.
To create more plants from just the one you have. To multiply, to increase the number of plants of the same type.
