That shows the minimum level to unlock the Roulette, because in both cases you need to have unlocked at least two of the duties included in the roulette to unlock the roulette itself. The Leveling Roulette is unlockable at level 16 because the two lowest level dungeons included in it are Sastasha (level 15) and Tam-Tara (level 16). But it then also includes many other dungeons and trials (once you unlock them individually), eventually ranging all the way from 15 to 59. Similarly, the Guildhest Roulette is unlockable at level 10, because that's the level of its two lowest level hests. It then includes all the others as well, ranging from 10 to 40.
There will eventually be other Duty Roulettes to unlock. The next one you'll unlock is Main Scenario Roulette, which includes just two dungeons (both level 50) that form the climax of the original ARR storyline. Then there is a Trials Roulette, including trials ranging from levels 49-60 (the roulette unlockable at 50, once you've done two of them). There is a Level 50 Roulette and Level 60 Roulette including a bunch of dungeons that are all at their stated level. (Unlike the others, these are only unlocked once you've run all the dungeons they include rather than once you've done two of them.) Then at endgame, there's also an Expert Roulette for the dungeons included in the most recent patch. (This one changes each patch cycle, with new ones added, and the previous moved into Level 60 Roulette.) And if you ever become a Mentor, there's a Mentor Roulette.
Summon III brings Ifrit-Egi as soon as you've unlocked Summoner. Initially, Summon and Summon II still bring the carbuncle pets from Arcanist until you unlock Titan-Egi and Garuda-Egi from the level 35 and 45 SMN quests respectively. Ifrit-Egi is stronger than Emerald Carbuncle. Once you have Garuda-Egi it becomes a harder choice. Each pet has its advantages. I'm no expert at the job, but I believe Garuda-Egi is considered better most of the time, but Ifrit-Egi is slightly better for quick fights without a lot of movement. (At least that seemed to be the consensus the last time I was reading up on that particular debate.) Plus some players like Ifrit-Egi better as easier to position.