On how/if I should ask my supervisor about lead authorship?
Yes, it is appropriate to ask, but it may not be best to demand. But personalities can get in the way of ethics, as many posts here show. "I worked pretty hard on this and having first authorship would give me a big career boost." That could work. Much better than simply demanding it as a right, even when it might be considered so. 

But, having some publication, no matter where you appear, is better than none. And don't think of this as do or die. There will be other papers and your professor's good opinion of you is worth more than first authorship on an early paper. 

But yes, it is appropriate to ask. It won't be rude unless you make it rude. 



Ideally these things are worked out before the research begins, but it often isn't. And the  power imbalance between professor and student gets in the way as does ego.