To clarify on what Dorgath said: once you reach rank 1, champion, you automatically get to keep it for the rest of the week, even if you lose every single battle after that. Then, when the reset happens on Mondays, you receive a nice reward based on what rank you achieved. The list above tells you what you get depending on what rank you reach.
To answer your second question: the offer to buy the troops at the end of the arena is available if you want to buy the troops you used for that run at level 15. That is to say, if you didn’t have the troop already, it would show up in your troop list already at level 15 - nice eh? The gem cost is determined by how many souls it would take to level up these troops to 15. If you don’t have any of the three troops at that level, the gem cost is quite high, because you are paying the gem costs to buy the needed souls right now, with this purchase - it’s intended to be convenient. If you already have some or all of the troops at that level, the gem cost is reduced accordingly - all the way down to just 1 gem if you already possess all 3 troops and have already leveled them to 15.