Hero Stars
Every hero has stars under their portrait. This is an approximate value of how well the hero stacks up against other heroes. Generally, the higher the stars, the better. However increasing this value gets exponentially difficult but the payoff is huge and a very noticeable jump in power could be seen visually in the Stats page, and in actual combat.
Hero Ascension
Hero Ascension can be done by collecting the appropriate Evos listed in their Ascend page. Ascending a hero gives them a fair stat boost and some new abilities be it passive, active, or both. All heroes can only be ascended twice and the cost of the second ascension is usually steep in Evo costs.
Hero Speed
Upon selecting your party members, you may notice colored numbers show up on their portraits. Green numbers denote Fast characters who attack first. Yellow numbers are the normal speed characters that attack after the fast characters and before the slow ones. Red numbers are of slow heroes. They attack last. The order you select the heroes also affect the order in which the characters with the same speed attacks. For example, if you select two fast heroes, the first one you selected will go first then the second one will go after. The order in which all your party members take action is also displayed numerically by 1-2-3-4. When attacking other players, the defending team always goes first. Meaning their Fast heroes will always attack first, their normal heroes will attack before your normal heroes do and so on.