Also OG ICRPG had no initiative. You sat down at the table. Person to the left of the GM always goes first; continue clockwise. If the players are surprised, GM goes first. For the entire SESSION you stay in turn order. This gives each player a voice.
Even when the session is ‘open’, you still control the table as if there is a turn order which makes the more aggressive talkative player get reigned in and brings the quieter player to the forefront. Usually the quiet players are quiet because they are waiting their turn. This clockwise turn order really shines.
In terms of your question regarding bonuses, stats (STR, DEX, CON, etc.) is your D20 bonus when attempting to do something and effort (basic, weapon, magic, etc.) is the damage you do at the task. This can be ANYTHING. You have to think outside of the D&D damage only mindset. Picking a lock, breaking open a door, hitting someone. All of these tasks can have Hearts (HP) and your players are attempting to do effort (damage) to overcome the obstacles you create.
The cool part about checks and effort is the addition of the timer. When a locked door has 2 Hearts of effort, the room timer is on 2, and dark critters are swarming into the room while the thief tries to pick the lock… Suddenly every player is doing what they can to protect the thief on their turn and then watching with anticipation when the thief rolls against the door lock later on their own turn. It brings everyone into the scene way more than D&D does (in my opinion).
Mainly look at a character sheet. Left side stats – roll to succeed. Right side effort – roll to deal effort (damage). Each are independent of one another when it comes to bonuses.
I recommend you trying the trial scenario solo in the Master Edition to get the best feel for how it is done.