Congrats on your lovely orchid plant. You asked, "Should I repot my beautiful orchid plant?" There is no need to repot an orchid that is flowering. The new stems growing upward may have more blooms so just wait and enjoy the show. After it is done flowering you should continue to give the plant daylight (near an East or North window is best) and do not make the mistake of overwatering. Look at the roots and if they are full and green they do not need water. If you do decide to repot your orchid after it blooms do so using only potting soil or bark chips made for orchids. They like to have small pots for their large roots so your orchid may be happy for years in the pot it came in. In the photo that you sent it looks like the long gray "stems"  facing outward or downward are actually roots from the plant. They will not bloom and you can cut them off or let them grow. For more information on repotting orchids, click this link for a video from Elizabeth Morse, one of our staff contributors. And if you have time for more, Abbi Hayes, another contributor, recounts her experience with her first successful orchid. Keep growing, Marianne Binetti