George, good questions. I've refereed a lot of Traveller, but I'll admit this doesn't come that often. My players have likely significantly underused this feature of the combat system.
First, combat is one of many circumstances that one could use a leadership skill check. That said, your questions pertain to combat, so here's how I would handle it. The rules don't actually specify any of this. If you read the rules literally, a Leadership check is just one more feature of combat that is on top of all the other actions. I think that would be taking the rules a little too literally, but this is just one referee's opinion. Traveller requires a lot of referee rulings on the fly.
Traveller combat allows for one significant action and one minor action, or three minor actions, per combat round. Then there are "free actions" and "reactions", that don't count towards these limits, and are only limited by referee discretion. I would rule that the leadership check can be made during the traveller's turn in combat (per the initiative rolls). Whether that leadership roll is a significant action, minor action, or free action depends on what the traveller is trying to accomplish. In other words, role play it. If its a quick word of encouragement ("Kill 'em all! Remember the Beowulf!") or instructions ("kill the psion first!"), then I would say that Leadership skill check is a minor action or free action. My ruling might depend on what the other minor action that traveller wants to do at the same time. If the player thinks its a free action, then ruling should be based on: can you attack (significant action), drop to a crouch (minor action), and do this Leadership check all at the same time? Because that's what a free action is. Remember that drawing a weapon counts as a minor action as well.
Could the leadership check be a reaction? I think so. Yelling ("cover Pookey!") after Pookey goes down from enemy fire I could see being a reaction, i.e. an action in response to the enemy's attack that round that doesn't count against the limits. Depending on the order of initiative, these boons might be used the current turn or the next. In other words, I wouldn't limit which traveller could use the boon based on who has already used their significant action that round.
If the player is trying to use boons for a bunch of different players in different positions, i.e. those at his side, a sniper on the hill, and the medic that needs to leave cover to treat someone, I'd rule that he/she is giving multiple commands and that counts for his/her significant action for that round.
The number of boons given has to be the total effect, not the effect X number of travellers. That would be way too much.
Can these boons, per your example of 5 boons and only three companions, be carried over to the next round? I would say yes in most cases, but I'd make the player dole them out right away (2 for you, 2 for you, sorry, only 1 for you) or dole them out myself as the ref. Can the leader really choose after the fact which companion was inspired for 6 seconds vs the one who was inspired for 12? I don't think so, so I'd let them carry over on these terms, but I wouldn't let the either player (the leaders or the boon recipient) just store a boon to be used in a tight spot 8 rounds later.
How often can the check be made? That's a tough one. Once per combat? Once every three rounds? I don't know. I could see an argument for the Leader directing combat and giving constant orders and encouragement (a very strong case can be made that this would be use of Tactics: Military rather than Leadership), but in such a circumstance I again count that leadership check as a significant action, meaning it takes the place of the Leader's own attack each round it is used.
One last thought: if someone tries to use leadership more than once while hiding behind hard cover themselves: nope. Can't see what's happening, can't lead.
Those answers are likely more ambiguous than you were hoping for, and I suspect others have radically different opinions, but I hope that helps.
