It varies from mode to mode. When you're battling in the Colosseums, first round, the rules are pre-set and could be either single or double depending on the specific rules for each Colosseum (the battling styles from area to area vary as well). As for Round 1 levels, they generally use L.30 as the starting point. From there the opponent(s) Pokemon will match the level of your highest Pokemon.
Round 2 is a bit different because often times it allows you to change the rules (ie. set whether you want single or double battle, and put the level cap at L.50 All). For areas like the revamped Stargazer Colosseum, tho, you'll still be stuck to whatever rules they give you.
Hope that helps answer a few questions.