Now to the questions:
Well, here's my responses at least, take them for what you will.
Q1 - When a NPC has results with threaths left, what should we do? If we apply Strain, it may become wounds if there is no Strain Threshold, is that correct?
A1 - Nominally correct, though as others have said the Threat can be used a variety of ways beyond just inflicting Strain. Perhaps the attacker left themselves wide-open on their attack, providing the next PC that attacks that NPC a boost die on the PC's attack roll. Perhaps the NPC took cover, but when they shot at the PCs, they left themselves too open, thus negating the effect of that cover. If the NPC rolled a lot of Threats (3 or more), perhaps they fumble their weapon in all the excitement and thus have to stoop down to pick it back up (mechancially, the NPC just fell prone).
Q2 - Having a Triumph on rolling the initiative, does it do anything? It's just a success, right?
A2 - It can be used to upgrade an ally's first skill check in the combat encounter (including that of the person that rolled it as a basic effect, or maybe even be used to bump an NPC's high result down lower in the initiative order as a means of "turning the tide of battle," or even be spent to provide the PCs with a notable advantage at the start of a fight, such as giving all the PCs the benefits of cover for the opening round. Triumphs are very much like rolling natural 20's in D&D or any other d20 game, so feel free to let the players have a little leeway in describing how that Triumph affects the scene in a positive fashion for the PCs.
Q3 - PC Roll for combat, no success, but 3 Advantage, he can still use them? I assume the same for Threats.
A3 - Yep, the PC can spend those Advantages however they wish, such as providing a boost die to one or more players, including themselves, on their next action. it could be used to cause a target to drop their weapon (since the disarm effect only costs 3 Advantage and doesn't require you to actually hit and deal damage to the target), or it could be used to negate some advantage the enemy has (like cover) or even to give the PC a boost to their own defense until their next turn. Quite frankly, if a PC was restricted to only spending Advantages if they scored a success, things would really suck for PCs that are operating out of their element (i.e. making checks for skills they have no ranks and/or few Ability dice in). And some does hold true with Threats, which can be spent regardless of the success or failure of the roll, making it possible to fail but come out with some kind of edge or to succeed but suffer a drawback.
Q4 - When a NPC rolls advantage/threaths, the same benefits that the PC have can be applied? Though, most NPC in the first encounters don't have strain Threshold, they can't gain/regain Strain, so only boost die would apply?
A4 - Pretty much.
Q5 - Does a Thriumph can always be used to trigger a critical?
A5 - That's one of the predominant uses of a Triumph in combat, given most weapons require at least 3 Advantages in order to trigger a Critical Hit. But even if the attack misses (note that a Triumph doesn't guarentee success on a roll), the Triumph can still be spent for other things.
Hope these answers help, even if only a little.