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There are two Arcade games that fit the description and have similar names, which I think are also on the Sega Saturn. One of them is called "Tant-R" (released 1992), and my guess is that "Sega Ages Vol. 1: Shukudaigan Tant-R" (Saturn) is the same game.
The other is called "Ichidant-R" (released 1994), which I'm guessing is the same as the game you are talking about - "Sega Ages: Rouka ni Ichidant-R"
Tant-R was also released on Sega's Game Gear and MegaDrive consoles in 1994, and Ichidant-R was released on the MegaDrive in 1995.
EDIT - Oh, you wanted some info on how to play some of the minigames? Well, if "Ichidant-R" is the same, then you are in luck, because there is a English version (clone) on the Arcade. I played a bit of it just then, and some of the mini-games included completing a rocket by filling in the missing pieces, braking in a car to stop at the edge of a cliff, and finding which houses a thief had recently robbed. Hope this sounds familiar to you. 
EDIT2: And I think Sando-R (1997) is the third of the series |