Hi @Shinerplunderer,
For the lag issues...when you experience lag, is it normally when you play on WiFi, data, or both? Rivals is generally more stable on data so, if it happens often on WiFi, you can try switching to data to see if it is better.
As your player level increases, you'll get additional counters to the units, including Zone Troopers. This is intentional, giving new players a chance to slowly learn the game and how all the units work. As for being able to play without internet, Rivals is about the player-vs-player combat, which does require the game to be played online. Doesn't meant that it couldn't happen, but the focus right now is on that PvP combat 🙂