For each participant in a battle, there is one turn in every round. A turn is the segment of time in each round that is alloted to that participant to take their three non-triggered actions (standard, move, minor).
Any other action that a character takes will occur during another participant's turn, due to events triggered by the actions taken by the active participant. (This trigger may be a function of the power held by the character, or an effect of the action by the active participant, i.e. leader granting a MBA.) None of these triggered actions are "turns". Some special cases of these triggered actions have limitations, such as the "once per turn" of OAs and the "once per round" of immediate actions. All triggered actions take place within the time frame of the action of the active participant that initiated the trigger. Triggers resolve in the order they are activated, with the exception of immediate interrupts, which resolve immediately before the action that triggered them.
Turn 1
Standard -> Leader grants MBA to 2 allies.
Trigger(1) -> Ally 1 takes MBA against Bladesinger.
Trigger(2) -> Bladesinger takes MBA against Ally 1 as OA.
Trigger(1) -> Ally 2 takes MBA against Bladesinger.
Trigger(2) -> Bladesinger would take MBA against Ally 2, but has already used an OA this turn.
Move -> Leader
Minor -> Leader
Turn 2
Standard ->
etc.
I don't believe there's a specific ruling as to how to resolve chains of triggers, or how to resolve actions that involve multiple parts (multi-attacks, leader powers where you attack and grant a move). I think, in general, for any power with multiple parts, you resolve one part, all triggers generated by that one part, and then the next part of the action. For example, if you use a power that lets an ally shift and make an attack. You can let the ally shift first, ally shifts into flanking position, and then you can make the attack with combat advantage.