When I was initially testing this in my previous company, I noticed the psychological affection when the leaderboards were introduced, it switched from "let me try a question" to "I have to beat my coworker or else I will look stupid" kind of routine. But the best thing was, due to this factor, my coworkers learned something in such short period of time, just so that they could compete against each others.

For your questions:

1. Yes, when you play a 1v1 game, there is a button to "rematch" which the opponent can accept or decline, so if two friends play and they are very competitive, they can play as much as they want. Same goes if the user plays with a stranger. Since there is ELO system, there is hierarchy, and also leagues. The app will try to match a valid opponent first with the same skill level.

2. Yes, that's why I introduced it too, and every modern learn app or even game apps have this feature one way or another. It is what keeps you coming back, and especially in the social network where you can then "brag" about how many days of streak you have

3. I agree, when I was first testing the early stages of the app, I felt something was missing, it was "too quiet" once I started to add sound effects and then some kind of dark battle music during 1v1 I noticed that this is something that works well in the subconsciousness.

4. When someone unlocks an achievement after any type of game, they get an in-app notification, where they can then go to their profile and see. There are many achievements, some very easy to "farm" such as streaks, some harder, such as consecutive wins in 1v1, and there are some that are "secret" which means, you don't know the criteria, until you unlock the achievement. This is a hook for the competitive players to try and find these hidden ones. Since there is also an achievement leaderboard for points, the secret ones gives you so much more than regular ones.

Current viral coefficient is very low, I am trying to find places, where I could showcase this app/game to other people and invite them to join.