Advice required for Jailbreak map

The thing with "minigames" is that there is no clear rule for how to make one. But you will need to understand the various entity classes that the game has and be creative in how you combine them.

Elaborating on what Henke said, minigames tend to be made out of what we call logic entities. There are two kinds: point entities and brush entities. Point entities are the little icons you see in Hammer, that occupy a specified point in a map. Commonly-used point entities are logic_timer, logic_case, tf_team_round_timer, logic_auto, logic_relay. Brush entities are brush volumes that can be used as solid walls or floors that can change solidity, colour, position and so on, or act as a trigger, for example trigger_multiple.

You can create a new point entity using the Entity tool, clicking in oneof the viewports and pressing Return/Enter. The default entity is usually a spawn point, and you can change it by double-clicking and typing in a new class in the field in the top left. To make a brush entity, you create a new brush, select it and press Ctrl+T to tie it to an entity. Then type the brush entity you want in the field (the default is func_detail).

My advice is to decompile existing maps and go and look at the logic of the minigames. Double-click each entity and check its Input and Output tab. If you'd like to see more available inputs and outputs for each entity, click the Help button on its Class Info page, or visit the Valve Developer Community wiki.

Here is an example minigame for you to study. Players are teleported on to the four platforms at the start, via the point_teleport entities. A trigger_once that covers all of the minigame starts the game. One func_brush platform flashes red. The players must jump to it using the small platform in the centre. After a short amount of time, the func_door gates close, and func_door spikes come through the floor of the other platforms, with a trigger_hurt parented to them, killing anyone left behind. It's a simple minigame that tests the player's jumping skills and reactions. It was designed for Deathrun, where all the participants are on the same team, and teammate collision is turned off, so outside of that environment it will probably face problems.

I think the best course of action is for you to design a simple minigame and research what you need to make it. Does it have moving brushes? Does it have hurt triggers? Think about these elements and look for entities that can give you what you want.