Is yoga a religion? If so, will it conflict with my religion?
No, yoga is not a religion. Conventional religion is primarily a matter of belief. In yoga however, practice is primary – not belief. It’s perfectly fine to be a yogi and follow your own religion.
Is it valuable and necessary to study Sanskrit in order to understand yoga history and philosophy?
Studying Sanskrit opens a door for you, as you’ll be able to read the original texts. You’ll always get a deeper understanding by reading the original. However, there are many very good translations and secondary sources, so don’t sweat it out if you don’t have the time to learn Sanskrit.