1. From me:
When you're driving your car, isn't it annoying when the driver in front of you puts his turn signal on long before he needs to turn? You become fixated on that signal because you don't know when or where you will have to slow down in order to accommodate him.
The same is true when you dance, when you pique or balance or even chassee. Some dancers flex their toes in anticipation of stepping up to the turn or out to the balance and what do we see? An ugly flexed turn signal.
I'm going now! Nope, here I go. Yes, here it is, here is my pique arabesque!
This is a particular pet peeve of mine, as a teacher and as an audience member. There is the esthetic of it (awkward and ugly) and the technical aspect (your foot isn't pointed or straight). Always - always -always point your feet all the way down to your toes. The aim is to melt the foot into the floor with every step and to roll through the demi-pointe softly. When you pique, stab those pointed toes into the floor and only bend them when you absolutely have to. It will look much better and the line will be complete.
2. From student:
Why would a teacher tell me to work in 3rd position instead of 5th? Which is better? Does it matter?
Third position is kind of a midway point: the heel of the working leg sits at the arch of the standing leg, rather than the toe. It can be useful if you are brand new to ballet (although I never use it with my new students) or are injured, as the turnout is not as forced and the knees can fit more comfortably, if necessary.
However, it is really more of a transitional position, as we usually think of working through 3rd on the way from 2nd or 1st to 5th when we do tendu or degage. It can help students feel the tops of the legs closing more tightly. I use it to emphasize a closure on glissade for instance, which can often be quite wide and loose for new students.
Is it better? No. It's useful but not better. For one thing, when you do not close your feet to 5th, you are not engaging your inner thighs so center work like allegro will not be as smooth or as quick as you'd like. By working in 5th at the barre, you are more likely to feel and engage the muscles you need to use to stabilize yourself in the center for adagio as well.
Does it matter? If you are injured, by all means, work in 3rd until you can comfortably tighten to 5th. Teachers who insist on 3rd are concerned with forced turnout and about the potential for rotating the knees too tightly and ultimately developing tendonitis or other knee pain. But if you work in your turnout and do not force it, you should be able to work in 5th rather than 3rd.